If the sum of linear angles at a common vertex is 180˚, then the angles are supplementary. Even if two right angles are added, equal to 180˚, the pair is known as a supplementary pair of angles.
If one angle out of a pair of linear angles is x, then the other angle is given by 180-x. This linearity remains the same for all the pairs of supplementary angles.
This property is also valid for trigonometric functions like-
From the given image, we can say that the pair of angles BOA and AOC are supplementary angles because their sum is equal to 180˚.
We can also find the other angle if only one of these angles is given. For example, consider only 60 degrees was given, we can find the other angle by 180-60 = 120˚.
When the sum of two angles is equal to 90˚, then the angles are said to be complementary angles. So even if you add two angles and form a right angle, the two angles are known to be complementary.
Complementary angle phenomenon is valid in trigonometry as well. The ratios are given as-
In the above image, we can see that AOD and DOB are complementary angles because their sum is equal to 90˚.
Also, in this image, angles POQ and ABC can be called complementary angles because their sum adds up to 90 degrees.
Find the values of angles P and Q, if angle P and angle Q are supplementary angles such that angle P = 2x+10 and angle Q is 6x-46
We know, the sum of angles of a supplementary pair is equal to 180˚.
Therefore, ∠P + ∠Q = 180˚
(2x + 10) + (6x - 46) = 180˚
8x - 36 =180
8x = 216
x = 27
Therefore, ∠P = 2(27) + 10 = 64˚ and ∠Q = 6(27) - 46 =116˚.
Given that two angles are supplementary in nature. The value of the larger angle is 5 degrees more than 4 times the measure of the smaller angle. Find out the value of a larger angle in degrees.
We need to consider the two supplementary angles as x (larger) and y (smaller).
From the information above, x = 4y+5
We know the sum of angles is 180˚ if they are supplementary.
x + y = 180˚
(4y + 5) + y = 180˚
5y + 5 = 180˚
5y = 175˚ = 35˚
Therefore, the larger angle x = 4(35) + 5 = 145˚