Question

the angle in one regular polygon is to that in other as 3:2 and number of side in first is twice that in the second determine the number of side of two polygon​

Answer 1

Answer:

8 and 4

Step-by-step explanation:

Suppose the number of sides in the first polygon be 2x and The number of sides in the second polygon be x.

As we know that, angle of an n-sided regular polygon = [(n - 2)/n]π radian

The angle of the first polygon = [(2x - 2)/2x]π = [(x - 1)/x]π radian

The angle of the second polygon = [(x - 2)/x]π radian

Hence, [(x - 1)/x]π/[(x - 2)/x]π = 3/2 (x - 1)/(x - 2) = 3/2 Now, upon cross-multiplication we get, 2x – 2 = 3x – 6 3x - 2x = 6 - 2 x = 4

∴ Number of sides in the first polygon = 2x = 2(4) = 8

Thus, the number of sides in the second polygon = x = 4

Hope it helps you!!