# Linear Pair: Definition, Theorem & Example

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• 1:21 Application
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Lesson Transcript

Jennie has eight years experience teaching high school math and has a Master's degree in Education Leadership.

In this lesson, we'ill discuss how a linear pair is formed and what characteristics apply to angles that create a linear pair. We'lll also go through a few examples in which we solve for the missing angle. At the end of the lesson, test yourself with a quiz.

## Definition

A linear pair is a pair of adjacent, supplementary angles. Adjacent means next to each other, and supplementary means that the measures of the two angles add up to equal 180 degrees.

As mentioned, adjacent angles are angles that are next to each other. If you are sitting next to someone in class or on the bus, you could say that you are adjacent to them. More specifically, adjacent angles share a vertex and have a common side.

Supplementary angles are any pair of angles that add to equal 180 degrees. Let's say you have to make a certain amount of money each month in order to pay all of your bills, but you only make a portion of that money at your regular job. You might find yourself looking for additional employment in order to supplement your current earnings. Your two jobs add to equal the amount needed to pay your bills in the same way that two supplementary angles add to equal 180 degrees.

Here is an example of adjacent, supplementary angles that work together to create a linear pair.

## Lines

Another important fact is that a line measures 180 degrees. So, a pair of adjacent, supplementary angles creates a line. Have you ever noticed how the name gives it away? A 'line-ar pair is a pair of angles that creates a line.

## Application

You may encounter problems that ask you to solve for the missing angle using a linear pair. As we have discussed, a linear pair adds up to equal 180 degrees. If you know the measure of one of the two angles, then you can subtract that measure from 180 degrees to get the measure of the other angle.

For example, let's say that angle A measures 75 degrees. What is the measure of angle B if this is a linear pair?

Remember, you cannot assume to know measurements based on the pictures that may appear in your textbook or on a test. You can only work based on the information that is given. This forces you to apply the concepts you have learned instead of relying on a visual.

Solution

180 - 75 = 105

So, angle B measures 105 degrees.

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