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Linear Pairs

Two adjacent angles that form a straight line.

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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.

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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, 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.

PSQ and QSR are a linear pair.

mPSRmPSQ+mQSRmPSQ+mQSR=180=mPSR=180

Example A

What is the value of each angle?

These two angles are a linear pair, so they are supplementary, or add up to 180. Write an equation.

(7q46)+(3q+6)10q4010qq=180=180=220=22

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

mABD=7(22)46=108mDBC=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. However, they are supplementary, 120+60=180.

Example C

Name one linear pair in the diagram below.

One example is INM and MNL.

Watch this video for help with the Examples above.

CK-12 Foundation: Chapter1LinearPairsB

Vocabulary

Adjacent angles are two angles that have the same vertex, share a side, and do not overlap. 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.

Guided Practice

1. What is mINL?

2. What is mLNK?

3. If mINJ=63, find mMNI.

Answers:

1. 180

2. 90

3. 18063=117

Interactive Practice

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.

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

  1. 54
  2. 32
  3. 104
  4. 71
  5. 149
  6. x

For 12-16, find the value of x.

Vocabulary

Adjacent Angles

Adjacent Angles

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.

Image Attributions

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