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Linear Pair of Angles: Definition and Examples | EDU.COMEDU.COMResourcesBlogGuidePodcastPlanBackHomesvg]:size-3.5">Math Glossarysvg]:size-3.5">Linear Pair of AnglesLinear Pair of Angles: Definition and ExamplesTable of ContentsLinear Pair of Angles: Definition, Examples and Properties Definition of Linear Pair of Angles

A linear pair of angles is formed when two adjacent angles share a common vertex and have one common arm, with their non-common arms forming a straight line. These angles always add up to 180°180°180°, making them supplementary angles. The term "linear" refers to their arrangement along a straight line, as they together form a straight angle. When two lines intersect at a single point, they create four angles, and any two adjacent angles among these form a linear pair.

Linear pairs of angles have several important properties. First, the angles in a linear pair are always supplementary (add up to 180°180°180°). Second, they are always adjacent angles with a common vertex and a common arm. Third, their non-common sides are opposite rays that form a straight line. The linear pair postulate states that if two angles form a linear pair, they are supplementary. However, the converse is not true - supplementary angles do not necessarily form a linear pair if they are not adjacent.

Examples of Linear Pair of Angles Example 1: Identifying Linear Pair of Angles in Intersecting Lines Problem:

Observe the diagram and identify the linear pair of angles where lines AB and XY intersect at point C.

Identifying Linear Pair of Angles in Intersecting Lines

Step-by-step solution:

Step 1, Look at what happens when two lines intersect. When lines AB and XY intersect at point C, they form four angles around point C.

Step 2, Remember what makes a linear pair. Any two adjacent angles that form a straight line (180°180°180°) will be a linear pair.

Step 3, Find all possible linear pairs. The linear pairs of angles are:

∠ACY\angle ACY∠ACY and ∠BCY\angle BCY∠BCY ∠ACX\angle ACX∠ACX and ∠ACY\angle ACY∠ACY ∠ACX\angle ACX∠ACX and ∠BCX\angle BCX∠BCX ∠BCX\angle BCX∠BCX and ∠BCY\angle BCY∠BCY Example 2: Finding Angle Measures in a Linear Pair with Given Ratio Problem:

If two angles forming a linear pair are in the ratio of 7:11, then find the measure of each of the angles.

Step-by-step solution:

Step 1, Let's name our angles using the ratio. If the ratio is 7:11, we can call the angles 7x°7x°7x° and 11x°11x°11x°, where xxx is a value we need to find.

Step 2, Use the linear pair property. Since these angles form a linear pair, they must add up to 180°180°180°: 7x°+11x°=180°7x° + 11x° = 180°7x°+11x°=180°

Step 3, Combine like terms and solve for xxx:

18x°=180°18x° = 180°18x°=180° x=10x = 10x=10

Step 4, Find each angle by multiplying by xxx:

First angle = 7×10=70°7 \times 10 = 70°7×10=70° Second angle = 11×10=110°11 \times 10 = 110°11×10=110° Example 3: Finding an Unknown Angle in a Linear Pair Problem:

Angles ∠ABC\angle ABC∠ABC and ∠DBC\angle DBC∠DBC form a linear pair of angles. Find the measure of ∠ABC\angle ABC∠ABC when ∠DBC\angle DBC∠DBC measures 48°48°48°.

Finding an Unknown Angle in a Linear Pair

Step-by-step solution:

Step 1, Remember the key property of linear pairs. Since angles in a linear pair are supplementary, they add up to 180°180°180°.

Step 2, Write an equation using this property:

m∠ABC+m∠DBC=180°m\angle ABC + m\angle DBC = 180°m∠ABC+m∠DBC=180°

Step 3, Substitute the known angle measure:

m∠ABC+48°=180°m\angle ABC + 48° = 180°m∠ABC+48°=180°

Step 4, Solve for the unknown angle:

m∠ABC=180°−48°m\angle ABC = 180° - 48°m∠ABC=180°−48° m∠ABC=132°m\angle ABC = 132°m∠ABC=132° Comments(3)DDadOf3BoysNovember 5, 2025I've used this clear def of linear pair of angles with my students. It made the concept easy to grasp, great resource!

MMomOf4GirlsNovember 4, 2025This glossary page on linear pairs of angles is great! It helped my students grasp the concept easily. Thanks for the clear def and examples.

NNatureLover85September 16, 2025I’ve been using this page to help my kids with their geometry homework, and the clear definition and examples of linear pairs made a big difference! It’s so easy to follow and explain now.

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