What if you were given two angles of unknown size and were told they are complementary? How would you determine their angle measures? After completing this Concept, you'll be able to use the definition of complementary angles to solve problems like this one.

### Watch This

Watch this video beginning at around the 3:20 mark.

James Sousa: Angle Basics--Complementary Angles

Then watch the first part of this video.

James Sousa: Complementary Angles

### Guidance

Two angles are
**
complementary
**
if they add up to
. Complementary angles
**
do not
**
have to be
*
congruent
*
or
*
next to each other
*
.

#### Example A

The two angles below are complementary. . What is ?

Because the two angles are complementary, they add up to . Make an equation.

#### Example B

The two angles below are complementary. Find the measure of each angle.

The two angles add up to . Make an equation.

However, you need to find each angle. Plug back into each expression.

#### Example C

Find the measure of an angle that is complementary to if is .

Because complementary angles have to add up to , the other angle must be .

### Guided Practice

Find the measure of an angle that is complementary to if is:

**
Answers:
**

- Because complementary angles have to add up to , the other angle must be .
- Because complementary angles have to add up to , the other angle must be .
- Because complementary angles have to add up to , the other angle must be .
- Because complementary angles have to add up to , the other angle must be .

### Practice

Find the measure of an angle that is complementary to if is:

Use the diagram below for exercises 8-9. Note that .

- Name two complementary angles.

- If , find .

For 10-11, determine if the statement is true or false.

- Complementary angles add up to .
- Complementary angles are always .