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Linear Pairs

Two adjacent angles that form a straight line.

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Linear Pairs

What if you were given two angles of unknown size and were told they form a linear pair? How would you determine their angle measures? After completing this Concept, you'll be able to use the definition of linear pair to solve problems like this one.

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CK-12 Linear Pairs

Guidance

Two angles are adjacent if they have the same vertex, share a side, and do not overlap 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 (add up to ). and are a linear pair.

Example A

What is the measure of each angle?

These two angles are a linear pair, so they add up to .

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. They are supplementary because they add up to : .

Example C

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

Because linear pairs have to add up to , the other angle must be .

CK-12 Linear Pairs

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Guided Practice

Use the diagram below. Note that .

1. Name one linear pair of angles.

2. What is ?

3. What is ?

4. If , find .

Answers:

1. and

2.

3.

4.

Explore More

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

  1. Linear pairs are congruent.
  2. Adjacent angles share a vertex.
  3. Adjacent angles overlap.
  4. Linear pairs are supplementary.
  5. Supplementary angles form linear pairs.

For exercise 6, find the value of .

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

Answers for Explore More Problems

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

Vocabulary

Adjacent Angles

Adjacent Angles

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

linear pair

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

Diagram

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

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