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Supplementary Angles

Supplementary Angles - Definition, Types, Supplementary and Complementary Angles Difference


Supplementary is a term used to refer to something that completes or fills another thing. Supplementary is derived from the Latin word ‘supplere’, which refers to filling something. Supplementary angles are thus a set of angles that complete each other to form 180-degrees. Supplementary angles are those that range from 0 to 180 degrees. Angles 60° and 120°, for example, are supplementary because combining 120° and 60° yields 180°. When the two supplementary angles are connected, they produce a straight line and a straight angle. However, it should be emphasised that the two additional angles do not have to be next to each other. As a result, any two angles can be supplementary if their total is exactly equal to 180°.

In Mathematics, the definition of supplementary is related to angles that are combined and together make a straight angle. This implies that two angles are considered to be supplementary angles when they sum up to 180 degrees. If two angles are supplementary, then either one of its angles is less than 90-degree (acute angle), and another angle is greater than 90-degree (obtuse angle), or both the angles are right angles, i.e., 90-degree in measure.

When formulated, the supplementary angles are expressed as follows: ∠K + ∠L = 180°. This formula aids in determining the values of the supplementary angle. If one of the values is known and another value has to be determined, then we can rearrange the formula as ∠K = 180° - ∠L. See the diagram below for a better comprehension of the summation of pair of angles.

There exist two types of supplementary angles:

Adjacent angles: The adjacent supplementary angles contain a common arm and base with each other. Non-adjacent angles: The non-adjacent supplementary angles do not share a common base and arm. They are detached from each other. Similarly, there is another set of angles known as complementary angles. A complementary angle is a pair of two angles that add up to 90 degrees and create a right angle.

Difference between Supplementary and Complementary Angles




The total sum of angles in supplementary angles is 180-degrees.

The total sum of angles in complementary angles is 90-degrees.

The supplementary angles are in the form of a straight line.

The complementary angles are in the form of a triangle, especially a right-angled one.

K + L = 180°.

K + L = 90°.

The supplement of any angle is 180 – angle given.

The complement of any angle is 90 – angle provided.

For example, if you cut a circle along its diameter, you get a semicircle having supplementary angles.

For example, if you cut a square along any of its diagonals, you get two right-angled triangles having complementary angles.

To remember what supplementary means, always keep in mind the “S” of the word “Supplementary”; this “S” can be denoted as ‘straight’. Hence you will remember that Supplementary angles form straight angles.  

To remember what complementary means, always keep in mind the ‘C’ of the word “complementary”; this “C” can be denoted as ‘Corner’. Hence you will remember that complementary angles form corner angles (90-degrees).


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