Question

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

Answer 1

Answer:

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 · 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.