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In geometry, pairs of angles can relate to each other in several ways.

In this lesson, we will learn

- about complementary angles
- about supplementary angles
- how to solve problems involving complementary and supplementary angles

Related Topics: 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

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

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:

TheCinComplementary stands forCorner, 90˚

TheSinSupplementary stands forStraight, 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.

Step 1: Make sure that the angles are complementary

Step 2: Setup a solvable equation

Step 3: Solve the equation

Complementary 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.

What it means for angles to be complementary and supplementary and do a few problems to find complements and supplements for different angles.

Create a system of linear equations to find the measure of an angle knowing information about its complement and supplement.

1. The measure of an angle is 14 degrees less than the measure of its complement. Find the measures of the two angles.

2. The measure of an angle is 6 degrees more than twice the measure of its supplement. Find the measures of the two angles.

3. The measure of the supplement of an angle is 20 degrees less than 4 times the measure of the angle. Find the measures of the two angles.

4. The supplement of an angle is 12 more than 3 times the complement. Find the angle, the complement and the supplement.

You can use the Mathway widget below to practice Algebra or other math topics. Try the given examples, or type in your own problem. Then click "Answer" to check your answer.