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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


Two angles are adjacent if they have the same vertex, share a side, and do not overlap PSQ and QSR 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 180). PSQ and QSR 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 180.


Plug in q to get the measure of each angle. mABD=7(22)46=108 mDBC=180108=72

Example B

Are CDA and DAB 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 180: 120+60=180.

Example C

Find the measure of an angle that forms a linear pair with MRS if mMRS is 150.

Because linear pairs have to add up to 180, the other angle must be 180150=30.

CK-12 Linear Pairs


Guided Practice

Use the diagram below. Note that NK¯¯¯¯¯¯IL.

1. Name one linear pair of angles.

2. What is mINL?

3. What is mLNK?

4. If mINJ=63, find mMNI.


1. MNL and LNJ

2. 180

3. 90

4. 18063=117

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 x.

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

  1. 61
  2. 23
  3. 114
  4. 7
  5. 179
  6. z

Answers for Explore More Problems

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


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.


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

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