Question

The ratio of each exterior angle to each interior angle of a regular polygon is 2:3 Find the number of sides of the polygon

Answer 1

Answer:

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Step-by-step explanation:

The measure of each interior angle is (n-2)(180/n) and the measure of each exterior angle is 360/n.  

So, 2/3 = 360/n ÷ (n-2)(180/n)  

      2/3 = (360/n) x n/(180n-360)  

      2/3 = 360/[180(n-2)]  

      2/3 = 2/(n-2)  

Cross multiply:  2(n-2) = 6  

                          2n-4 = 6  

                          2n = 10

So, n = 5  

The polygon is a regular pentagon.

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