Linear Pair of Angles

What is linear pair of angles?

Two angles form a linear pair if they have; 

A common arm

A common vertex

Their interiors do not overlap

The sum of two angles is 180°.

Therefore, linear pair of angles are adjacent angles whose non-common arms are opposite rays. 


All adjacent angles do not form a linear pair.

Linear Pair of angles

From the above figure we can observe; OX and OY are two opposite rays and ∠XOZ and ∠YOZ are the adjacent angles. Therefore, ∠XOZ and ∠YOZ form a linear pair. 

If you measure ∠XOZ and ∠YOZ with the help of the protractor, you will find the sum of their measures equal to 180°.

Thus, the sum of the angles in a linear pair is 180°.

Worked-out problems on Linear Pair of angles:

In the given figure, ∠AOC and ∠ BOC form a linear pair if x - y = 60°, find the value of x and y.

Linear Pair of angles


Given x - y = 60° ………… (i)

We know that, x + y = 180° ………… (ii)

Adding (i) and (ii)

2x = 240°

x = 240°/2

Therefore, x = 120°

Since, x - y = 60°

or, 120° - y = 60°

or, 120° - 120° - y = 60° - 120°

or, -y = -60°

Therefore, y = 60°

 Lines and Angles

Fundamental Geometrical Concepts


Classification of Angles

Related Angles

Some Geometric Terms and Results

Complementary Angles

Supplementary Angles

Complementary and Supplementary Angles

Adjacent Angles

Linear Pair of Angles

Vertically Opposite Angles

Parallel Lines

Transversal Line

Parallel and Transversal Lines

7th Grade Math Problems 

8th Grade Math Practice 

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