The central angle of the shaded sector is 10 degrees.
By formula,
[tex]\begin{gathered} \text{Area of Sector=}\frac{\theta}{360}\times\pi r^2 \\ \\ 16\pi=\frac{\theta}{360}\times\pi\times24^2 \\ \text{Cross multiply, we get} \\ 24^2\times\pi\times\theta=16\times\pi\times360 \\ \theta=\frac{16\times\pi\times360}{24^2\times\pi}=10^o \end{gathered}[/tex]
