### Theory:

Let us discuss what supplementary angles are.
Definition:
When the sum of the two angles is $$180^{\circ}$$, the angles are said to be supplementary angles. In the figure, $$\angle AOB$$ and $$\angle POQ$$ is a pair of angles.

The angles $$AOB$$ and $$POQ$$ are said to be supplementary if $$\angle AOB + \angle POQ = 180^{\circ}$$.
Example:
Verify if the given pair of angles are supplementary. Solution:

Given:

$$\angle XOY$$ $$=$$ $$130^{\circ}$$

$$\angle POQ$$ $$=$$ $$50^{\circ}$$

To verify:

Whether the given two angles are supplementary.

Verification:

Add the given two angles.

$$\angle XOY$$ $$+$$ $$\angle POQ$$ $$=$$ $$130^{\circ}$$ $$+$$ $$50^{\circ}$$

$$=$$ $$180^{\circ}$$

Since the sum of the two angles is $$180^{\circ}$$, by definition, the pair of angles $$XOY$$ and $$POQ$$ are supplementary.

Important!
When two angles are supplementary, each angle is said to be the supplement of the other.

Here $$\angle XOY$$ is the supplement of $$\angle POQ$$ and vice versa.

In other words, $$130^{\circ}$$ angle is the supplement of $$50^{\circ}$$ angle and vice versa.