Answer
$50.91^\circ$
Work Step by Step
The Area of sector is given by the formula
$A=\frac{\theta}{2}\cdot r^2$,where $\theta$ is in radians
Hence,
$100=\frac{\theta}{2}\cdot 15^2
\\100=\frac{\theta}{2}\cdot 225\\
100(2)=225\theta\\
200=225\theta\\
\frac{200}{225}=\theta\\
\frac{8}{9}=\theta$
$\\\\$Convert the angle to degrees to obtain:
$\frac{8}{9}\text{ rad}=\frac{8}{9}\text{rad}\cdot\frac{180^\circ}{\pi\text{ radians}} \approx 50.91^\circ.$
