Answer to Question #3258 in Geometry for vaishnavi gupta

Question

The ratio between an exterior angle and an interior angle is 2:3. Find the number of sides in the polygon.

Answer 1

The problem takes sence only if the polygon is regular. Let n be the number of sides. Then the n is the number of angles, too. As the ratio between an exterior angle and an interior angle is 2:3 we get

3α = 2(2π-α) ==> α = 4π/5.

Sum of interior angles of an n-sided polygon is (n-3)π. So,

nα = (n-3)π, or

4πn/5 = (n-3)π ==> n = 15.