Question

In the adjoining figure, $O$ is the centre of a circle. The area of sector $OAPB$ is $\frac{5}{18}$ of the area of the circle. Find $x$

Answer 1

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

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

$\Rightarrow \theta =\frac{5}{18}\times 360={100}^{\circ }$