{"id":122288,"date":"2022-03-23T16:56:40","date_gmt":"2022-03-23T11:26:40","guid":{"rendered":"https:\/\/www.aakash.ac.in\/blog\/?post_type=web-story&#038;p=122288"},"modified":"2022-08-19T15:39:11","modified_gmt":"2022-08-19T10:09:11","slug":"math-angle-between-two-lines-cbse-jee-maths-concept-note","status":"publish","type":"web-story","link":"https:\/\/www.aakash.ac.in\/blog\/web-stories\/math-angle-between-two-lines-cbse-jee-maths-concept-note\/","title":{"rendered":"Angle Between Two Lines | CBSE, JEE Maths Concept Note"},"content":{"rendered":"<p><html amp=\"\" lang=\"en\"><head><meta charSet=\"utf-8\"\/><meta name=\"viewport\" content=\"width=device-width,minimum-scale=1,initial-scale=1\"\/><script async=\"\" src=\"https:\/\/cdn.ampproject.org\/v0.js\"><\/script><script async=\"\" src=\"https:\/\/cdn.ampproject.org\/v0\/amp-story-1.0.js\" custom-element=\"amp-story\"><\/script><link 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template=\"vertical\" aspect-ratio=\"412:618\" class=\"grid-layer\"><\/p>\n<div class=\"page-fullbleed-area\">\n<div class=\"page-safe-area\">\n<div style=\"position:absolute;pointer-events:none;left:11.40777%;top:71.35922%;width:76.69903%;height:15.04854%;opacity:1\">\n<div id=\"anim-26cb31db-b75f-45bb-99dc-f9d0a12d16d3\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:1;--initial-transform:translate3d(-114.87342%, 0px, 0)\">\n<div id=\"anim-02665c47-670c-497c-8ce2-07614f3728ef\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:0;--initial-transform:none\">\n<div id=\"anim-e35676a9-4975-4ef4-898c-88563e2507cf\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:1;--initial-transform:scale(0.15)\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0;border-radius:0.6329113924050633% 0.6329113924050633% 0.6329113924050633% 0.6329113924050633% \/ 2.1505376344086025% 2.1505376344086025% 2.1505376344086025% 2.1505376344086025%;background-clip:content-box;background-color:#000\" id=\"el-0265250f-9c48-49f9-9412-cf47f527dc4e\">\n<p class=\"fill text-wrapper\" style=\"white-space:pre-wrap;overflow-wrap:break-word;word-break:break-word;margin:0.2074367088607595% 0;font-family:&quot;Merriweather&quot;,serif;font-size:0.372168em;line-height:1.2;text-align:center;padding:1.2658227848101267% 2.5316455696202533%;color:#000000\"><span><span style=\"color: #fff\">Angle Between Two Lines | CBSE, JEE Maths Concept Note<\/span><\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div style=\"position:absolute;pointer-events:none;left:11.40777%;top:90.93851%;width:41.74757%;height:4.04531%;opacity:1\">\n<div 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1)\",\"fill\":\"forwards\"}]<\/script><\/amp-story-animation><amp-story-grid-layer template=\"vertical\" aspect-ratio=\"412:618\" class=\"grid-layer\"><\/p>\n<div class=\"page-fullbleed-area\" style=\"background-color:#204e7c\">\n<div class=\"page-safe-area\">\n<div style=\"position:absolute;pointer-events:none;left:0;top:-9.25926%;width:100%;height:118.51852%;opacity:1\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0\" class=\"mask\" id=\"el-ec5023da-c6fa-4564-8e87-048b97749d7f\">\n<div style=\"position:absolute;width:100%;height:100%;left:0%;top:0%\" data-leaf-element=\"true\"><amp-img layout=\"fill\" src=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/03\/Angle-between-two-lines2.jpg\" alt=\"Angle between two lines2\" srcSet=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/03\/Angle-between-two-lines2.jpg 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style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:1;--initial-transform:translate3d(114.77986%, 0px, 0)\">\n<div id=\"anim-40ed8dbb-e1bd-42e7-adef-b2ac0144434e\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:0;--initial-transform:none\">\n<div id=\"anim-3a3717ed-acee-446b-8066-33f570710d28\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:1;--initial-transform:scale(0.15)\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0;border-radius:0.628930817610063% 0.628930817610063% 0.628930817610063% 0.628930817610063% \/ 1.0752688172043012% 1.0752688172043012% 1.0752688172043012% 1.0752688172043012%\" id=\"el-641bb672-0b5a-4f67-9424-a5177f4e5403\">\n<p class=\"fill text-wrapper\" 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type=\"application\/json\">[{\"selector\":\"#anim-23b858a2-7161-4d13-9f33-3139250f7264\",\"keyframes\":{\"transform\":[\"translate3d(-115.18988%, 0px, 0)\",\"translate3d(0px, 0px, 0)\"]},\"delay\":0,\"duration\":600,\"easing\":\"cubic-bezier(0.4, 0.4, 0.0, 1)\",\"fill\":\"both\"}]<\/script><\/amp-story-animation><amp-story-animation layout=\"nodisplay\" trigger=\"visibility\"><script type=\"application\/json\">[{\"selector\":\"#anim-c2e374b5-2185-4f05-9dfa-bc63edf71c38\",\"keyframes\":{\"opacity\":[0,1]},\"delay\":0,\"duration\":600,\"easing\":\"cubic-bezier(0.4, 0.4, 0.0, 1)\",\"fill\":\"both\"}]<\/script><\/amp-story-animation><amp-story-animation layout=\"nodisplay\" trigger=\"visibility\"><script type=\"application\/json\">[{\"selector\":\"#anim-79f4ba96-c77c-4922-9cd1-7037bc669643\",\"keyframes\":{\"transform\":[\"scale(0.15)\",\"scale(1)\"]},\"delay\":0,\"duration\":600,\"easing\":\"cubic-bezier(0.4, 0.4, 0.0, 1)\",\"fill\":\"forwards\"}]<\/script><\/amp-story-animation><amp-story-grid-layer template=\"vertical\" aspect-ratio=\"412:618\" class=\"grid-layer\"><\/p>\n<div class=\"page-fullbleed-area\" style=\"background-color:#272727\">\n<div class=\"page-safe-area\">\n<div style=\"position:absolute;pointer-events:none;left:0;top:-9.25926%;width:100%;height:118.51852%;opacity:1\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0\" class=\"mask\" id=\"el-a9eb0ac2-d684-4269-913c-e8f47c1267b3\">\n<div style=\"position:absolute;width:100%;height:100%;left:0%;top:0%\" data-leaf-element=\"true\"><amp-img layout=\"fill\" src=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/03\/Angle-between-two-lines3.jpg\" alt=\"Angle between two lines3\" srcSet=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/03\/Angle-between-two-lines3.jpg 720w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/03\/Angle-between-two-lines3-576x1024.jpg 576w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/03\/Angle-between-two-lines3-169x300.jpg 169w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/03\/Angle-between-two-lines3-150x267.jpg 150w\" sizes=\"(min-width: 1024px) 45vh, 100vw\" disable-inline-width=\"true\"><\/amp-img><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p><\/amp-story-grid-layer><amp-story-grid-layer template=\"vertical\" aspect-ratio=\"412:618\" class=\"grid-layer\"><\/p>\n<div class=\"page-fullbleed-area\">\n<div class=\"page-safe-area\">\n<div style=\"position:absolute;pointer-events:none;left:11.65049%;top:64.23948%;width:76.69903%;height:34.46602%;opacity:1\">\n<div id=\"anim-23b858a2-7161-4d13-9f33-3139250f7264\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:1;--initial-transform:translate3d(-115.18988%, 0px, 0)\">\n<div id=\"anim-c2e374b5-2185-4f05-9dfa-bc63edf71c38\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:0;--initial-transform:none\">\n<div id=\"anim-79f4ba96-c77c-4922-9cd1-7037bc669643\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:1;--initial-transform:scale(0.15)\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0;border-radius:0.6329113924050633% 0.6329113924050633% 0.6329113924050633% 0.6329113924050633% \/ 0.9389671361502347% 0.9389671361502347% 0.9389671361502347% 0.9389671361502347%\" id=\"el-53aa22a6-fd21-411c-80cc-e8e0a4f6bd8b\">\n<p class=\"fill text-wrapper\" style=\"white-space:pre-wrap;overflow-wrap:break-word;word-break:break-word;margin:0.198417721518987% 0;font-family:&quot;Merriweather&quot;,serif;font-size:0.355987em;line-height:1.2;text-align:left;padding:0;color:#000000\"><span><span style=\"color: #fff\">There are two angles between two intersecting lines:&nbsp;<\/span><br \/>\n<span style=\"color: #fff\">The<\/span><span style=\"text-decoration: underline; color: #fff\"> acute angle<\/span><span style=\"color: #fff\"> and the <\/span><span style=\"text-decoration: underline; color: #fff\">obtuse angle<\/span><span style=\"color: #fff\">.&nbsp;<\/span><br \/>\n<span style=\"color: #fff\">&#8211; For the angle between two lines, we consider the acute angle between the lines.<\/span><\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p><\/amp-story-grid-layer><\/amp-story-page><amp-story-page id=\"65309a1e-2b4b-4618-b8d0-6ed69a796062\" auto-advance-after=\"7s\"><amp-story-animation layout=\"nodisplay\" trigger=\"visibility\"><script type=\"application\/json\">[{\"selector\":\"#anim-1c432acb-12f6-4b6d-aa00-9d25c64293bb\",\"keyframes\":{\"transform\":[\"translate3d(-115.50632%, 0px, 0)\",\"translate3d(0px, 0px, 0)\"]},\"delay\":0,\"duration\":1300,\"easing\":\"cubic-bezier(0.4, 0.4, 0.0, 1)\",\"fill\":\"both\"}]<\/script><\/amp-story-animation><amp-story-animation layout=\"nodisplay\" trigger=\"visibility\"><script type=\"application\/json\">[{\"selector\":\"#anim-28e3204a-5665-4aeb-99d1-7ed6e7723df1\",\"keyframes\":{\"opacity\":[0,1]},\"delay\":0,\"duration\":1300,\"easing\":\"cubic-bezier(0.4, 0.4, 0.0, 1)\",\"fill\":\"both\"}]<\/script><\/amp-story-animation><amp-story-animation layout=\"nodisplay\" trigger=\"visibility\"><script type=\"application\/json\">[{\"selector\":\"#anim-1fd6d0f6-fd96-4ce9-afe3-ce434e048fea\",\"keyframes\":{\"transform\":[\"scale(0.15)\",\"scale(1)\"]},\"delay\":0,\"duration\":1300,\"easing\":\"cubic-bezier(0.4, 0.4, 0.0, 1)\",\"fill\":\"forwards\"}]<\/script><\/amp-story-animation><amp-story-grid-layer template=\"vertical\" aspect-ratio=\"412:618\" class=\"grid-layer\"><\/p>\n<div class=\"page-fullbleed-area\" style=\"background-color:#461b27\">\n<div class=\"page-safe-area\">\n<div style=\"position:absolute;pointer-events:none;left:0;top:-9.25926%;width:100%;height:118.51852%;opacity:1\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0\" class=\"mask\" id=\"el-7b3ddab1-84c5-442d-a793-56c45cc43d50\">\n<div style=\"position:absolute;width:100%;height:100%;left:0%;top:0%\" data-leaf-element=\"true\"><amp-img layout=\"fill\" src=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/03\/Angle-between-two-lines4.jpg\" alt=\"Angle between two lines4\" srcSet=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/03\/Angle-between-two-lines4.jpg 720w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/03\/Angle-between-two-lines4-576x1024.jpg 576w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/03\/Angle-between-two-lines4-169x300.jpg 169w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/03\/Angle-between-two-lines4-150x267.jpg 150w\" sizes=\"(min-width: 1024px) 45vh, 100vw\" disable-inline-width=\"true\"><\/amp-img><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p><\/amp-story-grid-layer><amp-story-grid-layer template=\"vertical\" aspect-ratio=\"412:618\" class=\"grid-layer\"><\/p>\n<div class=\"page-fullbleed-area\">\n<div class=\"page-safe-area\">\n<div style=\"position:absolute;pointer-events:none;left:11.8932%;top:71.35922%;width:76.69903%;height:22.81553%;opacity:1\">\n<div id=\"anim-1c432acb-12f6-4b6d-aa00-9d25c64293bb\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:1;--initial-transform:translate3d(-115.50632%, 0px, 0)\">\n<div id=\"anim-28e3204a-5665-4aeb-99d1-7ed6e7723df1\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:0;--initial-transform:none\">\n<div id=\"anim-1fd6d0f6-fd96-4ce9-afe3-ce434e048fea\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:1;--initial-transform:scale(0.15)\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0;border-radius:0.6329113924050633% 0.6329113924050633% 0.6329113924050633% 0.6329113924050633% \/ 1.4184397163120568% 1.4184397163120568% 1.4184397163120568% 1.4184397163120568%;background-clip:content-box;background-color:#000\" id=\"el-23838e29-fa46-403a-b837-1f13b809fe85\">\n<p class=\"fill text-wrapper\" style=\"white-space:pre-wrap;overflow-wrap:break-word;word-break:break-word;margin:0.198417721518987% 0;font-family:&quot;Merriweather&quot;,serif;font-size:0.355987em;line-height:1.2;text-align:center;padding:1.2658227848101267% 2.5316455696202533%;color:#000000\"><span><span style=\"color: #fff\">Knowing the slope of two lines or the equation of the two lines can be used to compute the angle between them.<\/span><\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div style=\"position:absolute;pointer-events:none;left:4.12621%;top:0;width:91.74757%;height:14.23948%;opacity:1\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0\" class=\"mask\" id=\"el-aa4e6ffe-af10-4aa5-9f81-116ce5eb1a0d\">\n<div class=\"fill\" style=\"background-color:#000;will-change:transform\"><\/div>\n<\/div>\n<\/div>\n<div style=\"position:absolute;pointer-events:none;left:11.8932%;top:2.42718%;width:73.05825%;height:9.54693%;opacity:1\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0;border-radius:0.6644518272425249% 0.6644518272425249% 0.6644518272425249% 0.6644518272425249% \/ 3.389830508474576% 3.389830508474576% 3.389830508474576% 3.389830508474576%\" id=\"el-932e8136-74ef-479a-9078-f2ca18e50b79\">\n<p class=\"fill text-wrapper\" style=\"white-space:pre-wrap;overflow-wrap:break-word;word-break:break-word;margin:-1.1991279069767442% 0;font-family:&quot;Roboto&quot;,&quot;Helvetica Neue&quot;,&quot;Helvetica&quot;,sans-serif;font-size:0.355987em;line-height:1.5;text-align:center;padding:0;color:#000000\"><span><span style=\"font-weight: 700; color: #fff\">How to Find the Angle between Two Lines?<\/span><\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p><\/amp-story-grid-layer><\/amp-story-page><amp-story-page id=\"ef87003b-9a80-4265-9e0f-b67abe15c678\" auto-advance-after=\"7s\"><amp-story-animation layout=\"nodisplay\" trigger=\"visibility\"><script type=\"application\/json\">[{\"selector\":\"#anim-0799c678-a553-4950-977d-aec614d8babc\",\"keyframes\":{\"transform\":[\"translate3d(114.87342%, 0px, 0)\",\"translate3d(0px, 0px, 0)\"]},\"delay\":0,\"duration\":1300,\"easing\":\"cubic-bezier(0.4, 0.4, 0.0, 1)\",\"fill\":\"both\"}]<\/script><\/amp-story-animation><amp-story-animation layout=\"nodisplay\" trigger=\"visibility\"><script type=\"application\/json\">[{\"selector\":\"#anim-3d2cfd84-00cb-487e-b6c0-3dcfbd769929\",\"keyframes\":{\"opacity\":[0,1]},\"delay\":0,\"duration\":1300,\"easing\":\"cubic-bezier(0.4, 0.4, 0.0, 1)\",\"fill\":\"both\"}]<\/script><\/amp-story-animation><amp-story-animation layout=\"nodisplay\" trigger=\"visibility\"><script type=\"application\/json\">[{\"selector\":\"#anim-a6a9ebe8-cc97-4e23-b534-52f71ac3ab19\",\"keyframes\":{\"transform\":[\"scale(0.15)\",\"scale(1)\"]},\"delay\":0,\"duration\":1300,\"easing\":\"cubic-bezier(0.4, 0.4, 0.0, 1)\",\"fill\":\"forwards\"}]<\/script><\/amp-story-animation><amp-story-grid-layer template=\"vertical\" aspect-ratio=\"412:618\" class=\"grid-layer\"><\/p>\n<div class=\"page-fullbleed-area\" style=\"background-color:#043b4a\">\n<div class=\"page-safe-area\">\n<div style=\"position:absolute;pointer-events:none;left:0;top:-9.25926%;width:100%;height:118.51852%;opacity:1\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0\" class=\"mask\" id=\"el-21be87f7-b985-4751-a054-6d915cfa2e79\">\n<div style=\"position:absolute;width:100%;height:100%;left:0%;top:0%\" data-leaf-element=\"true\"><amp-img layout=\"fill\" src=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/03\/Angle-between-two-lines5.jpg\" alt=\"Angle between two lines5\" srcSet=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/03\/Angle-between-two-lines5.jpg 720w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/03\/Angle-between-two-lines5-576x1024.jpg 576w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/03\/Angle-between-two-lines5-169x300.jpg 169w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/03\/Angle-between-two-lines5-150x267.jpg 150w\" sizes=\"(min-width: 1024px) 45vh, 100vw\" disable-inline-width=\"true\"><\/amp-img><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p><\/amp-story-grid-layer><amp-story-grid-layer template=\"vertical\" aspect-ratio=\"412:618\" class=\"grid-layer\"><\/p>\n<div class=\"page-fullbleed-area\">\n<div class=\"page-safe-area\">\n<div style=\"position:absolute;pointer-events:none;left:11.8932%;top:72.81553%;width:76.69903%;height:21.52104%;opacity:1\">\n<div id=\"anim-0799c678-a553-4950-977d-aec614d8babc\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:1;--initial-transform:translate3d(114.87342%, 0px, 0)\">\n<div id=\"anim-3d2cfd84-00cb-487e-b6c0-3dcfbd769929\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:0;--initial-transform:none\">\n<div id=\"anim-a6a9ebe8-cc97-4e23-b534-52f71ac3ab19\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:1;--initial-transform:scale(0.15)\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0;border-radius:0.6329113924050633% 0.6329113924050633% 0.6329113924050633% 0.6329113924050633% \/ 1.5037593984962405% 1.5037593984962405% 1.5037593984962405% 1.5037593984962405%\" id=\"el-32006551-6546-48f1-b87f-9eb83889303e\">\n<p class=\"fill text-wrapper\" style=\"white-space:pre-wrap;overflow-wrap:break-word;word-break:break-word;margin:0.198417721518987% 0;font-family:&quot;Merriweather&quot;,serif;font-size:0.355987em;line-height:1.2;text-align:center;padding:0;color:#000000\"><span><span style=\"color: #fff\">The angle between two lines can be computed from the slope by using the trigonometric tangent function.<\/span><\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p><\/amp-story-grid-layer><\/amp-story-page><amp-story-page id=\"e2ceefc6-f281-47e0-9ee8-569e5a2410ed\" auto-advance-after=\"7s\"><amp-story-animation layout=\"nodisplay\" trigger=\"visibility\"><script type=\"application\/json\">[{\"selector\":\"#anim-b4f9e527-67ed-4666-b8e5-bc09f8a13221\",\"keyframes\":{\"transform\":[\"translate3d(-115.50632%, 0px, 0)\",\"translate3d(0px, 0px, 0)\"]},\"delay\":0,\"duration\":1300,\"easing\":\"cubic-bezier(0.4, 0.4, 0.0, 1)\",\"fill\":\"both\"}]<\/script><\/amp-story-animation><amp-story-animation layout=\"nodisplay\" trigger=\"visibility\"><script type=\"application\/json\">[{\"selector\":\"#anim-39fd5ab3-b9bb-45ce-ab41-ab632f970f6d\",\"keyframes\":{\"opacity\":[0,1]},\"delay\":0,\"duration\":1300,\"easing\":\"cubic-bezier(0.4, 0.4, 0.0, 1)\",\"fill\":\"both\"}]<\/script><\/amp-story-animation><amp-story-animation layout=\"nodisplay\" trigger=\"visibility\"><script type=\"application\/json\">[{\"selector\":\"#anim-8bb7f47a-03a5-4c19-8753-0932f9a811de\",\"keyframes\":{\"transform\":[\"scale(0.15)\",\"scale(1)\"]},\"delay\":0,\"duration\":1300,\"easing\":\"cubic-bezier(0.4, 0.4, 0.0, 1)\",\"fill\":\"forwards\"}]<\/script><\/amp-story-animation><amp-story-grid-layer template=\"vertical\" aspect-ratio=\"412:618\" class=\"grid-layer\"><\/p>\n<div class=\"page-fullbleed-area\" style=\"background-color:#081d34\">\n<div class=\"page-safe-area\">\n<div style=\"position:absolute;pointer-events:none;left:0;top:-9.25926%;width:100%;height:118.51852%;opacity:1\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0\" class=\"mask\" id=\"el-08bdb875-2e48-432d-9e72-859c3bc29b19\">\n<div style=\"position:absolute;width:100%;height:100%;left:0%;top:0%\" data-leaf-element=\"true\"><amp-img layout=\"fill\" src=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/03\/angle-between-two-lines-6.jpg\" alt=\"angle between two lines 6\" srcSet=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/03\/angle-between-two-lines-6.jpg 720w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/03\/angle-between-two-lines-6-576x1024.jpg 576w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/03\/angle-between-two-lines-6-169x300.jpg 169w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/03\/angle-between-two-lines-6-150x267.jpg 150w\" sizes=\"(min-width: 1024px) 45vh, 100vw\" disable-inline-width=\"true\"><\/amp-img><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p><\/amp-story-grid-layer><amp-story-grid-layer template=\"vertical\" aspect-ratio=\"412:618\" class=\"grid-layer\"><\/p>\n<div class=\"page-fullbleed-area\">\n<div class=\"page-safe-area\">\n<div style=\"position:absolute;pointer-events:none;left:11.8932%;top:63.75405%;width:76.69903%;height:18.12298%;opacity:1\">\n<div id=\"anim-b4f9e527-67ed-4666-b8e5-bc09f8a13221\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:1;--initial-transform:translate3d(-115.50632%, 0px, 0)\">\n<div id=\"anim-39fd5ab3-b9bb-45ce-ab41-ab632f970f6d\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:0;--initial-transform:none\">\n<div id=\"anim-8bb7f47a-03a5-4c19-8753-0932f9a811de\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:1;--initial-transform:scale(0.15)\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0;border-radius:0.6329113924050633% 0.6329113924050633% 0.6329113924050633% 0.6329113924050633% \/ 1.7857142857142856% 1.7857142857142856% 1.7857142857142856% 1.7857142857142856%\" id=\"el-790d022a-c111-4935-91df-d128b9310e4c\">\n<p class=\"fill text-wrapper\" style=\"white-space:pre-wrap;overflow-wrap:break-word;word-break:break-word;margin:0.2074367088607595% 0;font-family:&quot;Merriweather&quot;,serif;font-size:0.372168em;line-height:1.2;text-align:left;padding:0;color:#000000\"><span><span style=\"color: #fff\">Let us consider two lines with slopes m1 and m2 respectively.&nbsp;<\/span><\/p>\n<p><\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p><\/amp-story-grid-layer><\/amp-story-page><amp-story-page id=\"111a0465-d436-44d1-bf08-a02d7f8aa901\" auto-advance-after=\"7s\"><amp-story-animation layout=\"nodisplay\" trigger=\"visibility\"><script type=\"application\/json\">[{\"selector\":\"#anim-faf8e515-da51-450a-8ad9-4eed1ac9aaac\",\"keyframes\":{\"transform\":[\"translate3d(114.87342%, 0px, 0)\",\"translate3d(0px, 0px, 0)\"]},\"delay\":0,\"duration\":1300,\"easing\":\"cubic-bezier(0.4, 0.4, 0.0, 1)\",\"fill\":\"both\"}]<\/script><\/amp-story-animation><amp-story-animation layout=\"nodisplay\" trigger=\"visibility\"><script type=\"application\/json\">[{\"selector\":\"#anim-4b2d9255-1d45-4e4d-88f3-4f0248e842d9\",\"keyframes\":{\"opacity\":[0,1]},\"delay\":0,\"duration\":1300,\"easing\":\"cubic-bezier(0.4, 0.4, 0.0, 1)\",\"fill\":\"both\"}]<\/script><\/amp-story-animation><amp-story-animation layout=\"nodisplay\" trigger=\"visibility\"><script type=\"application\/json\">[{\"selector\":\"#anim-71f1e22d-6771-4edc-88bd-77a63bdfa877\",\"keyframes\":{\"transform\":[\"scale(0.15)\",\"scale(1)\"]},\"delay\":0,\"duration\":1300,\"easing\":\"cubic-bezier(0.4, 0.4, 0.0, 1)\",\"fill\":\"forwards\"}]<\/script><\/amp-story-animation><amp-story-grid-layer template=\"vertical\" aspect-ratio=\"412:618\" class=\"grid-layer\"><\/p>\n<div class=\"page-fullbleed-area\" style=\"background-color:#27322b\">\n<div class=\"page-safe-area\">\n<div style=\"position:absolute;pointer-events:none;left:0;top:-9.25926%;width:100%;height:118.51852%;opacity:1\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0\" class=\"mask\" id=\"el-dcb8a8a9-05eb-409a-adab-8033494fd09b\">\n<div style=\"position:absolute;width:100%;height:100%;left:0%;top:0%\" data-leaf-element=\"true\"><amp-img layout=\"fill\" src=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/03\/angle-between-two-lines-7.jpg\" alt=\"angle between two lines 7\" srcSet=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/03\/angle-between-two-lines-7.jpg 720w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/03\/angle-between-two-lines-7-576x1024.jpg 576w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/03\/angle-between-two-lines-7-169x300.jpg 169w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/03\/angle-between-two-lines-7-150x267.jpg 150w\" sizes=\"(min-width: 1024px) 45vh, 100vw\" disable-inline-width=\"true\"><\/amp-img><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p><\/amp-story-grid-layer><amp-story-grid-layer template=\"vertical\" aspect-ratio=\"412:618\" class=\"grid-layer\"><\/p>\n<div class=\"page-fullbleed-area\">\n<div class=\"page-safe-area\">\n<div style=\"position:absolute;pointer-events:none;left:11.8932%;top:64.72492%;width:76.69903%;height:31.22977%;opacity:1\">\n<div id=\"anim-faf8e515-da51-450a-8ad9-4eed1ac9aaac\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:1;--initial-transform:translate3d(114.87342%, 0px, 0)\">\n<div id=\"anim-4b2d9255-1d45-4e4d-88f3-4f0248e842d9\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:0;--initial-transform:none\">\n<div id=\"anim-71f1e22d-6771-4edc-88bd-77a63bdfa877\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:1;--initial-transform:scale(0.15)\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0;border-radius:0.6329113924050633% 0.6329113924050633% 0.6329113924050633% 0.6329113924050633% \/ 1.0362694300518136% 1.0362694300518136% 1.0362694300518136% 1.0362694300518136%\" id=\"el-9673114a-11db-4f3a-b33d-1d92da2e340a\">\n<p class=\"fill text-wrapper\" style=\"white-space:pre-wrap;overflow-wrap:break-word;word-break:break-word;margin:1.2148734177215186% 0;font-family:&quot;BioRhyme&quot;,serif;font-size:0.355987em;line-height:1.2;text-align:left;padding:0;color:#000000\"><span><span style=\"color: #fff\">&#8211; Further, we can find the angle between the two lines if the equations are given.<\/span><br \/>\n<span style=\"color: #fff\">&#8211; Let the equations be l1=a1x+b1y+c1=0 and l2 = a2x+b2y+c2=0<\/span><\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p><\/amp-story-grid-layer><\/amp-story-page><amp-story-page id=\"dfe44ea0-5b10-4ba8-99dd-d8512fa263d4\" auto-advance-after=\"7s\"><amp-story-animation layout=\"nodisplay\" trigger=\"visibility\"><script type=\"application\/json\">[{\"selector\":\"#anim-9744d5f3-0a45-43f6-b8b0-cd08458501be\",\"keyframes\":{\"transform\":[\"translate3d(-115.18988%, 0px, 0)\",\"translate3d(0px, 0px, 0)\"]},\"delay\":0,\"duration\":1300,\"easing\":\"cubic-bezier(0.4, 0.4, 0.0, 1)\",\"fill\":\"both\"}]<\/script><\/amp-story-animation><amp-story-animation layout=\"nodisplay\" trigger=\"visibility\"><script type=\"application\/json\">[{\"selector\":\"#anim-24eb8aaf-5430-4b5c-9a91-7818ba4cd12f\",\"keyframes\":{\"opacity\":[0,1]},\"delay\":0,\"duration\":1300,\"easing\":\"cubic-bezier(0.4, 0.4, 0.0, 1)\",\"fill\":\"both\"}]<\/script><\/amp-story-animation><amp-story-animation layout=\"nodisplay\" trigger=\"visibility\"><script type=\"application\/json\">[{\"selector\":\"#anim-545b2d97-7d7f-4199-a4c6-7965e1626301\",\"keyframes\":{\"transform\":[\"scale(0.15)\",\"scale(1)\"]},\"delay\":0,\"duration\":1300,\"easing\":\"cubic-bezier(0.4, 0.4, 0.0, 1)\",\"fill\":\"forwards\"}]<\/script><\/amp-story-animation><amp-story-grid-layer template=\"vertical\" aspect-ratio=\"412:618\" class=\"grid-layer\"><\/p>\n<div class=\"page-fullbleed-area\" style=\"background-color:#182348\">\n<div class=\"page-safe-area\">\n<div style=\"position:absolute;pointer-events:none;left:0;top:-9.25926%;width:100%;height:118.51852%;opacity:1\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0\" class=\"mask\" id=\"el-e7f12270-7fd2-48e6-8728-b63e7527fe68\">\n<div style=\"position:absolute;width:100%;height:100%;left:0%;top:0%\" data-leaf-element=\"true\"><amp-img layout=\"fill\" src=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/03\/Angle-Between-two-lines-8-1.jpg\" alt=\"Angle Between two lines 8 (1)\" srcSet=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/03\/Angle-Between-two-lines-8-1.jpg 720w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/03\/Angle-Between-two-lines-8-1-576x1024.jpg 576w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/03\/Angle-Between-two-lines-8-1-169x300.jpg 169w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/03\/Angle-Between-two-lines-8-1-150x267.jpg 150w\" sizes=\"(min-width: 1024px) 45vh, 100vw\" disable-inline-width=\"true\"><\/amp-img><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p><\/amp-story-grid-layer><amp-story-grid-layer template=\"vertical\" aspect-ratio=\"412:618\" class=\"grid-layer\"><\/p>\n<div class=\"page-fullbleed-area\">\n<div class=\"page-safe-area\">\n<div style=\"position:absolute;pointer-events:none;left:11.65049%;top:68.77023%;width:76.69903%;height:34.46602%;opacity:1\">\n<div id=\"anim-9744d5f3-0a45-43f6-b8b0-cd08458501be\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:1;--initial-transform:translate3d(-115.18988%, 0px, 0)\">\n<div id=\"anim-24eb8aaf-5430-4b5c-9a91-7818ba4cd12f\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:0;--initial-transform:none\">\n<div id=\"anim-545b2d97-7d7f-4199-a4c6-7965e1626301\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:1;--initial-transform:scale(0.15)\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0;border-radius:0.6329113924050633% 0.6329113924050633% 0.6329113924050633% 0.6329113924050633% \/ 0.9389671361502347% 0.9389671361502347% 0.9389671361502347% 0.9389671361502347%\" id=\"el-416bf0a1-2b07-422a-a90b-096de559795c\">\n<p class=\"fill text-wrapper\" style=\"white-space:pre-wrap;overflow-wrap:break-word;word-break:break-word;margin:0.198417721518987% 0;font-family:&quot;Merriweather&quot;,serif;font-size:0.355987em;line-height:1.2;text-align:left;padding:0;color:#000000\"><span><span style=\"color: #fff\">&#8211; The angle between two lines that are parallel to each other and have equal slopes is zero degrees.<\/span><br \/>\n<span style=\"color: #fff\">-The distance between two parallel lines is at all times constant.<\/span><\/p>\n<p><\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p><\/amp-story-grid-layer><\/amp-story-page><amp-story-page id=\"635418e1-dfcb-42e1-a316-f36bc7b0c0dd\" auto-advance-after=\"7s\"><amp-story-animation layout=\"nodisplay\" trigger=\"visibility\"><script type=\"application\/json\">[{\"selector\":\"#anim-247fedaa-67af-4267-abaa-0bd5ad5141f2\",\"keyframes\":{\"transform\":[\"translate3d(-114.87342%, 0px, 0)\",\"translate3d(0px, 0px, 0)\"]},\"delay\":0,\"duration\":1300,\"easing\":\"cubic-bezier(0.4, 0.4, 0.0, 1)\",\"fill\":\"both\"}]<\/script><\/amp-story-animation><amp-story-animation layout=\"nodisplay\" trigger=\"visibility\"><script type=\"application\/json\">[{\"selector\":\"#anim-11a1bf80-d96d-471e-9bbc-ffb2720e5205\",\"keyframes\":{\"opacity\":[0,1]},\"delay\":0,\"duration\":1300,\"easing\":\"cubic-bezier(0.4, 0.4, 0.0, 1)\",\"fill\":\"both\"}]<\/script><\/amp-story-animation><amp-story-animation layout=\"nodisplay\" trigger=\"visibility\"><script type=\"application\/json\">[{\"selector\":\"#anim-79970092-c949-402f-8596-07c623fe8590\",\"keyframes\":{\"transform\":[\"scale(0.15)\",\"scale(1)\"]},\"delay\":0,\"duration\":1300,\"easing\":\"cubic-bezier(0.4, 0.4, 0.0, 1)\",\"fill\":\"forwards\"}]<\/script><\/amp-story-animation><amp-story-grid-layer template=\"vertical\" aspect-ratio=\"412:618\" class=\"grid-layer\"><\/p>\n<div class=\"page-fullbleed-area\" style=\"background-color:#272727\">\n<div class=\"page-safe-area\">\n<div style=\"position:absolute;pointer-events:none;left:0;top:-9.25926%;width:100%;height:118.51852%;opacity:1\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0\" class=\"mask\" id=\"el-f2872771-22f1-4b35-a583-4f94615e5888\">\n<div style=\"position:absolute;width:100%;height:100%;left:0%;top:0%\" data-leaf-element=\"true\"><amp-img layout=\"fill\" src=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/03\/mathematics-9.jpg\" alt=\"mathematics-9\" srcSet=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/03\/mathematics-9.jpg 720w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/03\/mathematics-9-576x1024.jpg 576w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/03\/mathematics-9-169x300.jpg 169w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/03\/mathematics-9-150x267.jpg 150w\" sizes=\"(min-width: 1024px) 45vh, 100vw\" disable-inline-width=\"true\"><\/amp-img><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p><\/amp-story-grid-layer><amp-story-grid-layer template=\"vertical\" aspect-ratio=\"412:618\" class=\"grid-layer\"><\/p>\n<div class=\"page-fullbleed-area\">\n<div class=\"page-safe-area\">\n<div style=\"position:absolute;pointer-events:none;left:11.40777%;top:73.46278%;width:76.69903%;height:21.52104%;opacity:1\">\n<div id=\"anim-247fedaa-67af-4267-abaa-0bd5ad5141f2\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:1;--initial-transform:translate3d(-114.87342%, 0px, 0)\">\n<div id=\"anim-11a1bf80-d96d-471e-9bbc-ffb2720e5205\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:0;--initial-transform:none\">\n<div id=\"anim-79970092-c949-402f-8596-07c623fe8590\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:1;--initial-transform:scale(0.15)\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0;border-radius:0.6329113924050633% 0.6329113924050633% 0.6329113924050633% 0.6329113924050633% \/ 1.5037593984962405% 1.5037593984962405% 1.5037593984962405% 1.5037593984962405%\" id=\"el-98995567-d60f-4bc7-aa41-3c030890c0fa\">\n<p class=\"fill text-wrapper\" style=\"white-space:pre-wrap;overflow-wrap:break-word;word-break:break-word;margin:0.198417721518987% 0;font-family:&quot;Merriweather&quot;,serif;font-size:0.355987em;line-height:1.2;text-align:left;padding:0;color:#000000\"><span><span style=\"color: #fff\">The angle between two lines are perpendicular to each other and have the product of their slopes equal to -1 is 90 degrees.<\/span><\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p><\/amp-story-grid-layer><\/amp-story-page><amp-story-page id=\"6a433abd-e311-4f3f-b96b-8a503662b108\" auto-advance-after=\"7s\"><amp-story-animation layout=\"nodisplay\" trigger=\"visibility\"><script type=\"application\/json\">[{\"selector\":\"#anim-4002805c-f7d3-465e-adac-bdd849957f3c\",\"keyframes\":{\"opacity\":[0,1]},\"delay\":0,\"duration\":1300,\"easing\":\"cubic-bezier(.3,0,.55,1)\",\"fill\":\"both\"}]<\/script><\/amp-story-animation><amp-story-animation layout=\"nodisplay\" trigger=\"visibility\"><script type=\"application\/json\">[{\"selector\":\"#anim-a946d8ec-0554-4f35-b021-ff97e6935287\",\"keyframes\":{\"transform\":[\"scale(0.3333333333333333)\",\"scale(1)\"]},\"delay\":0,\"duration\":1300,\"easing\":\"cubic-bezier(.3,0,.55,1)\",\"fill\":\"forwards\"}]<\/script><\/amp-story-animation><amp-story-grid-layer template=\"vertical\" aspect-ratio=\"412:618\" class=\"grid-layer\"><\/p>\n<div class=\"page-fullbleed-area\" style=\"background-color:#041f2a\">\n<div class=\"page-safe-area\">\n<div style=\"position:absolute;pointer-events:none;left:0;top:-9.25926%;width:100%;height:118.51852%;opacity:1\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0\" class=\"mask\" id=\"el-f2872771-22f1-4b35-a583-4f94615e5888\">\n<div style=\"position:absolute;width:100%;height:100%;left:0%;top:0%\" data-leaf-element=\"true\"><amp-img layout=\"fill\" src=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/03\/angle-between-two-lines-1-2.jpg\" alt=\"angle between two lines (1)\" srcSet=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/03\/angle-between-two-lines-1-2.jpg 720w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/03\/angle-between-two-lines-1-2-576x1024.jpg 576w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/03\/angle-between-two-lines-1-2-169x300.jpg 169w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/03\/angle-between-two-lines-1-2-150x267.jpg 150w\" sizes=\"(min-width: 1024px) 45vh, 100vw\" disable-inline-width=\"true\"><\/amp-img><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p><\/amp-story-grid-layer><amp-story-grid-layer template=\"vertical\" aspect-ratio=\"412:618\" class=\"grid-layer\"><\/p>\n<div class=\"page-fullbleed-area\">\n<div class=\"page-safe-area\">\n<div style=\"position:absolute;pointer-events:none;left:11.65049%;top:74.59547%;width:76.69903%;height:21.52104%;opacity:1\">\n<div id=\"anim-4002805c-f7d3-465e-adac-bdd849957f3c\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:0;--initial-transform:none\">\n<div id=\"anim-a946d8ec-0554-4f35-b021-ff97e6935287\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:1;--initial-transform:scale(0.3333333333333333)\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0;border-radius:0.6329113924050633% 0.6329113924050633% 0.6329113924050633% 0.6329113924050633% \/ 1.5037593984962405% 1.5037593984962405% 1.5037593984962405% 1.5037593984962405%\" id=\"el-d45eee70-6620-46ff-9f6d-08cd68dc165c\">\n<p class=\"fill text-wrapper\" style=\"white-space:pre-wrap;overflow-wrap:break-word;word-break:break-word;margin:0.198417721518987% 0;font-family:&quot;Merriweather&quot;,serif;font-size:0.355987em;line-height:1.2;text-align:left;padding:0;color:#000000\"><span><span style=\"font-weight: 700; color: #fff\">Example:<\/span><span style=\"color: #fff\"> Find the angle between the following two lines<\/span><br \/>\n<span style=\"color: #fff\">Line 1: 3x-2y = 4<\/span><br \/>\n<span style=\"color: #fff\">Line 2: x + 4y = 1<\/span><\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p><\/amp-story-grid-layer><\/amp-story-page><amp-story-page id=\"4772fea3-d563-4872-8154-5b911abaebbd\" auto-advance-after=\"7s\"><amp-story-grid-layer template=\"vertical\" aspect-ratio=\"412:618\" class=\"grid-layer\"><\/p>\n<div class=\"page-fullbleed-area\" style=\"background-color:#192348\">\n<div class=\"page-safe-area\">\n<div style=\"position:absolute;pointer-events:none;left:0;top:-9.25926%;width:100%;height:118.51852%;opacity:1\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0\" class=\"mask\" id=\"el-0dd23f17-75a8-4369-b087-06f9b3cd9868\">\n<div style=\"position:absolute;width:100%;height:100%;left:0%;top:0%\" data-leaf-element=\"true\"><amp-img layout=\"fill\" src=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/03\/angle-between-two-lines.jpg\" alt=\"angle between two lines\" srcSet=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/03\/angle-between-two-lines.jpg 720w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/03\/angle-between-two-lines-576x1024.jpg 576w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/03\/angle-between-two-lines-169x300.jpg 169w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/03\/angle-between-two-lines-150x267.jpg 150w\" sizes=\"(min-width: 1024px) 45vh, 100vw\" disable-inline-width=\"true\"><\/amp-img><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p><\/amp-story-grid-layer><amp-story-grid-layer template=\"vertical\" aspect-ratio=\"412:618\" class=\"grid-layer\"><\/p>\n<div class=\"page-fullbleed-area\">\n<div class=\"page-safe-area\"><\/div>\n<\/div>\n<p><\/amp-story-grid-layer><\/amp-story-page><amp-story-page id=\"6d46515c-29a8-476c-baab-1ecec57e217f\" auto-advance-after=\"7s\"><amp-story-grid-layer template=\"vertical\" aspect-ratio=\"412:618\" 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style=\"color: #fff\">Knowing the slope of two lines or the equation of the two lines can be used to compute the angle between 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