### Theory:

Let us discuss what linear pair of angles are.
Definition:
Linear pair is a type of angle formed by two adjacent angles, whose non-common sides are opposite rays.
In other words, the sum of the linear pair of angles is supplementary ($$180^{\circ}$$). In the figure, the sum of the linear angles $$POR$$ and $$ROQ$$ is equal to $$180^{\circ}$$.

That is, $$a + b = 180^{\circ}$$.
Example:
If $$x$$ and $$y$$ are the measures of linear pair of angles, then find the value of $$y$$ given $$x$$ $$=$$ $$65^{\circ}$$.

Solution:

Given that, $$x$$ $$=$$ $$65^{\circ}$$.

By the property of linear pair of angles, $$x$$ $$+$$ $$y$$ $$=$$ $$180^{\circ}$$.

$$\Rightarrow 65^{\circ} + y = 180^{\circ}$$

$$\Rightarrow y = 180^{\circ} - 65^{\circ}$$

$$\Rightarrow y = 115^{\circ}$$
Some real life examples:
The following are some real-life examples where we can observe linear pair of angles.

• The ladder makes a linear pair of angles with the ground. • The writing quill in the inked dip makes a linear pair of angle with the table. • The knife makes a linear pair of angle with the chopping board. 