Question

The ratio of the number of sides of two regular polygons is 1:2, and the ratio of the
sum of their interior angles is 3 : 8. Find the number of sides in each polygon.​

Answer 1

Answer:

Number of sides in polygon are 5 & 10

Step-by-step explanation:

Sum of interior angle of a polygon is given by

(n-2) * 180

Let say sides of polygons are  n  & 2n respectively

then Sum of interior angles = (n-2) * 180   & (2n-2) * 180

(n-2) * 180 / (2n-2) * 180   = 3/8

=> 8(n-2) = 3(2n -2)

=> 8n - 16 = 6n - 6

=> 2n = 10

=> n = 5

Number of sides in polygon are 5 & 10