Question #206635

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.


1
Expert's answer
2021-06-14T15:25:30-0400

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

The measure of each interior angle is (n2)180°n\dfrac{(n-2)180\degree}{n} and the measure of each exterior angle is 360°n.\dfrac{360\degree}{n}.

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


(n2)180°n360°n.=32\dfrac{\dfrac{(n-2)180\degree}{n}}{\dfrac{360\degree}{n}.}=\dfrac{3}{2}

2(n2)=3(2)2(n-2)=3(2)

n=5n=5


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