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.

**Note: **

All adjacent angles do not form a linear pair.

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.

**Solution: **

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**

**Some Geometric Terms and Results**

**Complementary and Supplementary Angles**

**Parallel and Transversal Lines**

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