### Linear Pairs

**Adjacent angles** are two angles that have the same vertex, share a side, and do not overlap. In the picture below, and are adjacent.

A **linear pair** is two angles that are adjacent and whose non-common sides form a straight line. If two angles are a linear pair, then they are supplementary.

and are a linear pair.

#### Measuring Angles

What is the value of each angle?

These two angles are a linear pair, so they are supplementary, or add up to . Write an equation.

So, plug in to get the measure of each angle.

#### Identifying Linear Pairs

1. Are and a linear pair? Are they supplementary?

The two angles are not a linear pair because they do not have the same vertex. However, they are supplementary, .

2. Name one linear pair in the diagram below.

One example is and .

### Examples

The following Examples use the diagram below:

#### Example 1

What is ?

=

#### Example 2

What is ?

=

#### Example 3

If , find .

### Review

For 1-5, determine if the statement is true or false.

- Linear pairs are congruent.
- Adjacent angles share a vertex.
- Adjacent angles overlap.
- Linear pairs are supplementary.
- Supplementary angles form linear pairs.

Find the measure of an angle that forms a linear pair with if is:

For 12-16, find the value of .

### Review (Answers)

To view the Review answers, open this PDF file and look for section 1.9.