Question

two regular polygon are such that the ratio between the number of sides is 12 and the ratio between the measure of interior angle is 30 for find the number of side of a polygon ​

Answer 1

Answer:

Given :

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

Ratio of interior angles is 3:4

To find :

Side of each polygon

Solution:

The interior angle of the polygon is given by,

((x-2)/x) * 180

Let us take the sides as a and 2a.

substituting in 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

4а-8 = 3а-3

⇒a=5