# Finding the measure of an angle given area and diameter.

Alright, so i've been trying to tackle this problem. The answer to this problem is 40 degrees (3). Now i'm trying to figure out how.

I decided to start with finding the area of the whole circle which is $9\pi$ cm$^2$ since the radius is 3 cm

but I do not how to proceed from there. Any ideas or hints?

• There is a formula that allows you to compute the shaded sector from the angle LOM and the radius of the circle. – Diego Jul 20 '16 at 5:13

The area of the shaded sector is $\frac{\theta}2 r^2$, where $\theta = \angle LOM$. Hence, $\theta = 4\pi/9$, so $\angle NOM = 5\pi/9$.
Now $\triangle NOM$ is isosceles at $O$, so $2\angle N = \pi - \angle NOM = 4\pi/9$, hence $\angle N = 2\pi/9 = 40^{\circ}$.