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# Linear Pairs

## Two adjacent angles that form a straight line.

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Estimated7 minsto complete
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Linear Pairs

What if you notice two angles in a picture that make a straight line? What information does this give you about the angles? After completing this Concept, you'll be able to apply the properties of linear pairs to help you solve problems.

### Watch This

CK-12 Foundation: Chapter1Linear PairsA

James Sousa: Linear Pairs

### Guidance

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.

#### Example A

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.

#### Example B

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, .

#### Example C

Name one linear pair in the diagram below.

One example is and .

Watch this video for help with the Examples above.

CK-12 Foundation: Chapter1LinearPairsB

1. What is ?

2. What is ?

3. If , find .

1.

2.

3.

### Explore More

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

1. Linear pairs are congruent.
2. Adjacent angles share a vertex.
4. Linear pairs are supplementary.
5. 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 .

### Answers for Explore More Problems

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

### Vocabulary Language: English

Two angles are adjacent if they share a side and vertex. The word 'adjacent' means 'beside' or 'next-to'.
Diagram

Diagram

A diagram is a drawing used to represent a mathematical problem.
linear pair

linear pair

Two angles form a linear pair if they are supplementary and adjacent.