[tex]\text{From the question, we are provided with the radius, r=15km, and the area of the sector to be 10}\pi km^2[/tex]
We would have to use the area of the sector and the radius provided to get the angle subtended at the centre of the circle.
Thus, we have:
[tex]\begin{gathered} A_{\sec tor}=\frac{\theta}{360}\times\pi\times r^2 \\ 10\pi=\frac{\theta}{360}\times\pi\times15^2 \\ 10\pi=\frac{\theta}{360}\times\pi\times15^2 \\ 10\pi=\frac{\theta}{360}\times\pi\times225 \\ \text{The }\pi\text{ cancels out each other, we have:} \\ 10=\frac{\theta}{360}\times225 \\ \theta=\frac{10\times360}{225} \\ \theta=16^0 \end{gathered}[/tex]
Hence, the angle measure is 16 degrees.
