Question

two regular polygons are such that the ratio between their number of sides is 1:2 and ratio of measure of interior angle is 3:8.find number of sides of each polygon

Answer 1

Given:

Two polygon in which the ratio between their number of sides is 1:2

Ratio of interior angle is 3:4

To find:

Side of each polygon

The interior angle of the polygon is given by,

(x-2)/x)*180

let us take the side as a and 2a

substituting the above formula , we get

((a-2)/a * 180/(2a-2/2a) *180=3/4

(a-2)/a * 2(a-1) =3/4

(a-2) / (a-1)=3/4

4a-8=3a-3

a=5