Some angles are said to have a relationship with each other. Identifying such angles and understanding the relationship they have with each other can help us solve mathematical problems.

Complementary Angles

Two angles are said to be complementary when the sum of their measures is $9 0^{\circ} .$

Here $∠ T S U$ and $∠ U S V$ are complementary angles since the sum of their measures equals the measure of $∠ T S V,$ which is a right angle.

Supplementary Angles

Two angles are supplementary when the sum of their measures is $18 0^{\circ} .$

In this example $∠ S P R$ and $∠ R P Q$ are two supplementary angles if the $S P Q$ is a straight line.

Adjacent Angles

When two angles are adjacent they have a common vertex and a common side.

Since both $∠ T S U$ and $∠ U S V$ have $S$ as a vertex and $S U$ as a side they are adjacent angles.

Vertical Angles

Two angles with sides that form two pairs of opposite rays are so called vertical angles.

In the diagram $∠ W M S$ and $∠ N M E$ are vertical angles. Also $∠ W M N$ and $∠ S M E$ form a pair of vertical angles.

Exercise