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# Complementary Angles

## Two angles that add to 90 degrees.

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Practice Complementary Angles
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Complementary Angles

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.

### Guidance

Two angles are complementary when they add up to $90^\circ$ . 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. $m \angle GHI = x$ . What is $x$ ?

Because the two angles are complementary, they add up to $90^\circ$ . Make an equation.

$x + 34^\circ = 90^\circ\\x = 56^\circ$

#### Example B

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

Again, the two angles add up to $90^\circ$ . Make an equation.

$8r + 9^\circ + 7r+ 5^\circ & = 90^\circ\\15r + 14^\circ & = 90^\circ\\15r & = 76^\circ\\r & \approx 5.1^\circ$

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

For $m \angle GHI$ : $8(5.1^\circ) + 9^\circ = 49.8^\circ$ , so $m \angle GHI \approx 49.8^\circ$ .

For $m \angle JKL$ : $7(5.1^\circ) + 5^\circ = 40.7^\circ$ , so $m \angle JKL \approx 40.7^\circ$ .

#### Example C

Name one pair of complementary angles in the diagram below.

One example is $\angle INJ$ and $\angle JNK$ .

Watch this video for help with the Examples above.

### Vocabulary

Two angles are complementary when they add up to $90^\circ$ .

### Guided Practice

Find the measure of an angle that is complementary to $\angle ABC$ if $m \angle ABC$ is

1. $45^\circ$
2. $82^\circ$
3. $19^\circ$
4. $z^\circ$

1. $45^\circ$

2. $8^\circ$

3. $71^\circ$

4. $90-z^\circ$

### Practice

Find the measure of an angle that is complementary to $\angle ABC$ if $m\angle ABC$ is:

1. $3^\circ$
2. $82^\circ$
3. $51^\circ$
4. $30^\circ$
5. $22^\circ$
6. $(x+y)^\circ$
7. $x^\circ$

Use the diagram below for exercises 8-9. Note that $\overline{NK} \perp \overleftrightarrow{IL}$ .

1. If $m\angle INJ = 60^\circ$ , find $m\angle KNJ$ .
2. If $m\angle INJ = 70^\circ$ , find $m\angle KNJ$ .

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

1. Complementary angles add up to $180^\circ$ .
2. Complementary angles are always $45^\circ$ .
3. Complementary angles are always next to each other.
4. Complementary angles add up to $90^\circ$ .
5. Two angles that make a right angle are complementary.
6. The two non-right angles in a right triangle are complementary.