# Central Angles

A
**
central angle
**
is an angle with its vertex at the center of a circle, with its sides containing two
radii
of the circle.

In the figure above, $\angle PZQ,\angle QZR$ , and $\angle RZP$ are central angles.

**
Sum of Central Angles:
**
The sum of the measures of the central angles of a circle with no points in common is
$360\xb0$
.

For example, in the figure above,

$m\angle PZR+m\angle RZQ+m\angle QZP=360\xb0$ .

**
Example:
**

Find the value of $x$ .

The sum of the measures of the central angles of a circle with no interior points in common is $360\xb0$ . So,

$\begin{array}{l}m\angle MON+m\angle NOP+m\angle POM=360\xb0\\ 50\xb0+90\xb0+x=360\xb0\end{array}$

Simplify.

$140\xb0+x=360\xb0$

Subtract $140\xb0$ from each side.

$x=220\xb0$