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.
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.
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