Answer
$A=\dfrac{\pi{r^2}\theta}{360^o}$
Work Step by Step
Recall:
(1) The area $A$ of a sector of a circle is givne by the formula $A=\dfrac{1}{2}r^2\theta$ where $r$=radius and $\theta$ is the central angle mesure in radians.
(2) To convert an angle measure from degree to radians, $\dfrac{\pi}{180^o}$
must be multiplied to the given radian measure.
Thus, the formula for the area of a sector of a circle when the angle measurement is in degrees is:
\begin{align*}
A&=\dfrac{1}{2}r^2\theta \left(\dfrac{\pi}{180^o}\right)\\\\
A&=\dfrac{\pi{r^2}\theta}{2(180^o)}\\\\
A&=\dfrac{\pi{r^2}\theta}{360^o}\\\\
\end{align*}
