Question

The ratio of exterior angle to interior angle of a regular polygon is 1:4. find the no.of sides of the polygon

Answer 1

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