# 8.2: Angle Pairs

**At Grade**Created by: CK-12

**Practice**Angle Pairs

Lily wants to change the hopscotch design so that each player's foot can only land in half of each box. Her plan is to draw a line from one corner of each box to the diagonal corner of each box. She takes out a protractor to measure half of a corner angle in Box 1. What should be the measure of half of a corner angle?

In this concept, you will learn how to identify and use angle pairs.

### Identifying and Using Angle Pairs

Two angles together are **angle pairs .** Sometimes, the measures of these angles form a special relationship. One special relationship is called

**complementary angles**. Complementary angles are angle pairs that add up to exactly \begin{align*}90^{\text{o}}.\end{align*}

Below are some pairs of complementary angles.

**Supplementary angles** are two angles that add up to exactly \begin{align*}180^{\text{o}}.\end{align*}

Let’s look at two examples.

Classify the following pairs of angles as either complementary or supplementary.

The sum of the angles in Figure 1 is **\begin{align*}180^{\text{o}}.\end{align*} 180o.** Therefore these angles are supplementary angles.

The sum of the angles in Figure 2 is **\begin{align*}90^{\text{o}}.\end{align*} 90o.** Therefore these angles are complementary angles.

Remember, complementary angles add up to \begin{align*}90^{\text{o}},\end{align*}

### Examples

#### Example 1

Earlier, you were given a problem about Lily, who wants to divide spaces in half by drawing a line from one corner to the diagonal corner.

Lily needs to figure out the value of half of a corner angle. If she divides a \begin{align*}90^{\text{o}}\end{align*}

First, what type of angle pair equals \begin{align*}90^{\text{o}}?\end{align*}

Complementary angles

Next, what is the value of half of \begin{align*}90^{\text{o}}\end{align*}

\begin{align*}45^{\text{o}}\end{align*}

Then, write the size of each angle.

\begin{align*}45^{\text{o}} \! , \ 45^{\text{o}}\end{align*}

The answer is that Lily will create complementary angles that each have a measure of \begin{align*}45^{\text{o}}.\end{align*}

#### Example 2

Solve the following problem by identifying the angle pair as complementary, supplementary or neither.

Angle \begin{align*}A = 36^{\text{o}} \! ,\end{align*}

First, add the values of the angles.

\begin{align*}36^{\text{o}} + 45^{\text{o}} = 81^{\text{o}}\end{align*}

Next, check to see if the sum is **\begin{align*}90^{\text{o}}\end{align*} 90o** or \begin{align*}180^{\text{o}}\end{align*}

The sum is \begin{align*}81^{\text{o}}.\end{align*}

Then, draw a conclusion.

Neither complementary nor supplementary.

The answer is neither.

**Identify the following angle pairs as complementary, supplementary or neither.**

#### Example 3

Angle \begin{align*}A = 23^{\text{o}},\end{align*}

First, add the values of the angles.

\begin{align*}23^{\text{o}} + 45^{\text{o}} = 68^{\text{o}}\end{align*}

Next, check to see if the sum is **\begin{align*}90^{\text{o}}\end{align*} 90o** or \begin{align*}180^{\text{o}}.\end{align*}

The sum is \begin{align*}68^o\end{align*}

Then, draw a conclusion.

Neither complementary nor supplementary.

The answer is neither.

#### Example 4

Angle \begin{align*}A = 45^{\text{o}} \!,\end{align*}

First, add the values of the angles.

\begin{align*}45^{\text{o}} + 45^{\text{o}} = 90^{\text{o}}\end{align*}

Next, check to see if the sum is **\begin{align*}90^{\text{o}}\end{align*} 90o** or \begin{align*}180^{\text{o}} \!.\end{align*}

The sum is \begin{align*}90^{\text{o}} \!.\end{align*}

Then, draw a conclusion.

The angles are complementary.

The answer is complementary angles.

#### Example 5

Angle \begin{align*}A = 103^{\text{o}} \!,\end{align*}

First, add the values of the angles.

\begin{align*}103^o + 77^o = 180^o\end{align*}

Next, check to see if the sum is **\begin{align*}90^{\text{o}}\end{align*}** or \begin{align*}180^{\text{o}}\!.\end{align*}

The sum is \begin{align*}180^{\text{o}}\!.\end{align*}

Then, draw a conclusion.

The angles are supplementary.

The answer is supplementary angles.

### Review

Identify whether the pairs below are complementary, supplementary or neither.

- An angle pair whose sum is \begin{align*}180^{\text{o}}\end{align*}
- Angle \begin{align*}A = 90^{\text{o}}\end{align*} Angle \begin{align*}B\end{align*} is \begin{align*}45^{\text{o}}\end{align*}
- Angle \begin{align*}C = 125^{\text{o}}\end{align*} Angle \begin{align*}B = 55^{\text{o}}\end{align*}
- An angle pair whose sum is \begin{align*}180^{\text{o}}\end{align*}
- An angle pair whose sum is \begin{align*}245^{\text{o}}\end{align*}
- An angle pair whose sum is \begin{align*}80^{\text{o}}\end{align*}
- An angle pair whose sum is \begin{align*}90^{\text{o}}\end{align*}
- An angle pair whose sum is \begin{align*}55^{\text{o}}\end{align*}
- An angle pair whose sum is \begin{align*}120^{\text{o}}\end{align*}
- An angle pair whose sum is \begin{align*}95^{\text{o}}\end{align*}
- An angle pair whose sum is \begin{align*}201^{\text{o}}\end{align*}
- An angle pair whose sum is \begin{align*}190^{\text{o}}\end{align*}

### Review (Answers)

To see the Review answers, open this PDF file and look for section 8.2.

### Resources

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In this concept, you will learn how to identify and use angle pairs.

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