Theory:

The pair of angles are classified into the following based on their relationship with each other.
• Complementary angles
• Supplementary angles
• Linear pair of angles and
• Vertically opposite angles

Let us discuss what complementary angles are.
Definition:
When the sum of the two angles is $$90^{\circ}$$, then the angles are called complementary angles.

In the figure, $$\angle AOB$$ and $$\amgle POQ$$ is a pair of angles.

The angles $$AOB$$ and $$POQ$$ are said to be complementary if $$\angle AOB + \angle POQ = 90^{\circ}$$.
Example:
Verify if the given pair of angles are complementary.

Solution:

Given:

$$\angle XOY$$ $$=$$ $$55^{\circ}$$

$$\angle POQ$$ $$=$$ $$35^{\circ}$$

To verify:

Whether the given two angles are complementary.

Verification:

$$\angle XOY$$ $$+$$ $$\angle POQ$$ $$=$$ $$55^{\circ}$$ $$+$$ $$35^{\circ}$$

$$=$$ $$90^{\circ}$$

Since the sum of the two angles is $$90^{\circ}$$, by definition, the pair of angles $$XOY$$ and $$POQ$$ are complementary.

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

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

In other words, $$55^{\circ}$$ angle is the complement of $$35^{\circ}$$ angle.