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Answer to Question #3258 in Geometry for vaishnavi gupta

Question #3258
The ratio between an exterior angle and an interior angle is 2:3. Find the number of sides in the polygon.
Expert's answer
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.

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