If the area of a sector of a circle is

We have given that area of the sector is $\frac{5}{18}$ of the area of the circle.

Therefore, area of the sector $=\frac{5}{18} \times$ area of the circle

$\therefore \frac{\theta}{360} \times \pi r^{2}=\frac{5}{18} \times \pi r^{2}$

Now we will simplify the equation as below,

$\frac{\theta}{360}=\frac{5}{18}$

Now we will multiply both sides of the equation by 360,

$\therefore \theta=\frac{5}{18} \times 360$

$\therefore \theta=100$

Therefore, sector angle is $100^{\circ}$.

Hence, the correct answer is option (c).