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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.  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.

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 .

Example 1

Name one linear pair of angles.

and

Example 2

What is ?

Example 3

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 4

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 5

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 .

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 .

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

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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