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Linear Pairs

Two adjacent angles that form a straight line.

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Linear Pairs

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.

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?

Examples

For Examples 1 and 2, use the diagram below. Note that NK¯¯¯¯¯¯¯¯¯IL.

Example 1

Name one linear pair of angles.

MNL and LNJ

Example 2

What is mINL?

180

Example 3

What is the measure of each angle?

These two angles are a linear pair, so they add up to 180.

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

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

Example 4

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 5

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.

Review

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

Review (Answers)

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

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    Vocabulary

    Adjacent Angles

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

    linear pair

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

    Diagram

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

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