In these lessons, we will learn
Related Pages
Pairs Of Angles
Types Of Angles
More Geometry Lessons
The following table gives a summary of complementary and supplementary angles. Scroll down the page if you need more explanations about complementary and supplementary angles, videos and worksheets.
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 | |
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˚. |
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
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.
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 explanations of complementary angles and supplementary angles:
This video describes complementary and supplementary angles with a few example problems. It will also explain a neat trick to remember the difference between complementary and supplementary angles.
Examples:
Step 1: Make sure that the angles are complementary.
Step 2: Setup a solvable equation.
Step 3: Solve the equation.
Example:
∠1 = 8x + 6<br
∠2 = 19x + 3
∠1 and ∠2 are complementary.
Solve for x.
Complementary Word Problem
How to solve a word problem about its angle and its complement?
Example:
The measure of an angle is 43° more than its complement. Find the measure of each angle.
What it means for angles to be complementary and supplementary and do a few problems to find complements and supplements for different angles.
Examples:
Find the measure of the complementary angle for each of the following angles:
a) 7°
b) 18°
c) 72°
Find the measure of the supplementary angle for each of the following angles:
a) 124°
b) 75°
Create a system of linear equations to find the measure of an angle knowing information about its complement and supplement.
Example:
The supplement of angle y measures 12x + 4 and the complement of the angle measures 6x. What is the
measure of the angle?
Examples:
Try the free Mathway calculator and
problem solver below to practice various math topics. Try the given examples, or type in your own
problem and check your answer with the step-by-step explanations.
We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.