## Adjacent Angles

Two angles having a common vertex and a common arm, such that the other arms of these angles are on opposite sides of the common arm, are called adjacent angles.

- is the common vertex
- $A\hat{O}B$ and $B\hat{O}C$ are adjacent angles.
- Arm BO separates the two angles.

## Complementary Angles

If the sum of the two angles is one right angle (i.e., 90^{o}), they are called complementary angles.

If the measure of $A\hat{O}C$ = a^{0 }, $C\hat{O}B$ = b^{0 }, then a^{0} + b^{0} = 90^{0 }.

Therefore $A\hat{O}C$ and $C\hat{O}B$ are complementary angles.

$A\hat{O}C$ is complement of $C\hat{O}B$

## Supplementary Angles

Two angles are said to be supplementary, if the sum of their measures is 180^{o}.

Example

Angles measuring 130^{o} and 50^{o} are supplementary angles.

Two supplementary angles are the supplement of each other.

## Vertically Opposite Angles

When two straight lines intersect each other at a point, the pairs of opposite angles so formed are called vertically opposite angles.

Angles $\angle{1}$ and $\angle{3}$ and angles $\angle{2}$ and $\angle{4}$ are vertically opposite angles. Vertically opposite angles are always equal.

## Bisector of an Angle

If a ray or a straight line passing through the vertex of that angle, divides the angle into two angles of equal measurement, then that line is known as the Bisector of that angle.

$B\hat{O}C$ = $C\hat{O}A$

And $B\hat{O}C$ + $C\hat{O}A$ = $A\hat{O}B$

And $A\hat{O}B$ = 2$B\hat{O}C$ = 2$C\hat{O}A$