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Linear Pairs

Two adjacent angles that form a straight line.

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Linear Pairs

Linear Pairs 

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

and are a linear pair.

Measuring Angles 

What is the value of each angle?

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

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

Identifying Linear Pairs

1. Are and 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, .

2. Name one linear pair in the diagram below.

One example is and .


The following Examples use the diagram below:

Example 1

What is ?


Example 2

What is ?


Example 3

If , find .



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 if is:

For 12-16, find the value of .

Review (Answers)

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

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Adjacent Angles Two angles are adjacent if they share a side and vertex. The word 'adjacent' means 'beside' or 'next-to'.
Diagram A diagram is a drawing used to represent a mathematical problem.
linear pair Two angles form a linear pair if they are supplementary and adjacent.

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