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Complementary Angles and Supplementary Angles

In geometry, pairs of angles can relate to each other in several ways. In this lesson we will explain complementary angles and supplementary angles.

Complementary Angles

Two angles are called complementary angles if the sum of their degree measurements equals 90 degrees (right angle). One of the complementary angles is said to be the complement of the other.
The two angles do not need to be together or adjacent. They just need to add up to 90 degrees. If the two complementary angles are adjacent then they will form a right angle.

∠ABC is the complement of ∠CBD

Example:
x and y are complementary angles. Given x = 35˚, find the value y.

Solution:
x + y = 90˚
35˚ + y = 90˚
y = 90˚ – 35˚ = 55˚

Worksheets for Complementary Angles

In a right triangle, the two acute angles are complementary. This is because the sum of angles in a triangle is 180˚ and the right angle is 90˚. Therefore, the other two angles must add up to 90˚.

Supplementary Angles

Two angles are called supplementary angles if the sum of their degree measurements equals 180 degrees (straight line) . One of the supplementary angles is said to be the supplement of the other.
The two angles do not need to be together or adjacent. They just need to add up to 180 degrees. If the two supplementary angles are adjacent then they will form a straight line.

∠ABC is the supplement of ∠CBD

Example:
x and y are supplementary angles. Given x = 72˚, find the value y.

Solution:
x + y = 180˚
72 ˚ + y = 180˚
y = 180˚ –72˚ = 108˚

Worksheets for Supplementary Angles

A mnemonic to help you remember:
The C in Complementary stands for Corner, 90˚
The S in Supplementary stands for Straight, 180˚

Have a look at the following videos for further explainations of complementary angles and supplementary angles.:

How to identify complementary and supplementary angles.

How to Find the Measure of Complementary Angles Using Algebra

Complementary Angles Word Problem
How to solve a word problem about its angle and its complement
The measure of an angle is 43 more than its complement. Find the measure of each angle.

Complementary and Supplementary Angles - Example 1.
What it means for angles to be complementary and supplementary and do a few problems to find complements and supplements for different angles.

Complementary and Supplementary Angles - Example 2.
Create a system of linear equations to find the measure of an angle knowing information about its complement and supplement.

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