Answer to Question #206635 in Geometry for Festus

Question

The ratio of the interior angle to the exterior angle of a regular polygon is 3:2. Find the number of side In the polygon.

Answer 1

Let $n=$ the nu ber of sides of a regular polygon.

The measure of each interior angle is $\dfrac{(n-2)180\degree}{n}$ and the measure of each exterior angle is $\dfrac{360\degree}{n}.$

Given that the ratio of the interior angle to the exterior angle of a regular polygon is 3:2

$$\dfrac{\dfrac{(n-2)180\degree}{n}}{\dfrac{360\degree}{n}.}=\dfrac{3}{2}$$

$$2(n-2)=3(2)$$

$$n=5$$