What if you knew that two angles together made a right angle? After completing this Concept, you'll be able to use what you know about complementary angles to solve problems about these angles.

### Watch This

CK-12 Foundation: Chapter1ComplementaryAnglesA

James Sousa: Complementary Angles

### Guidance

Two angles are **complementary** when they add up to . Complementary angles do not have to be congruent to each other, nor do they have to be 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.

Again, the two angles add up to . Make an equation.

However, this is not what the question asks for. You need to plug back into each expression to find each angle.

For : , so .

For : , so .

#### Example C

Name one pair of complementary angles in the diagram below.

One example is and .

Watch this video for help with the Examples above.

CK-12 Foundation: Chapter1ComplementaryAnglesB

### Vocabulary

Two angles are ** complementary** when they add up to .

### Guided Practice

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

**Answers:**

1.

2.

3.

4.

### Interactive Practice

### Practice

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

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

- If , find .
- If , find .

For 10-15, determine if the statement is true or false.

- Complementary angles add up to .
- Complementary angles are always .
- Complementary angles are always next to each other.
- Complementary angles add up to .
- Two angles that make a right angle are complementary.
- The two non-right angles in a right triangle are complementary.