cat 2022 Question 3

Question

Regular polygons A and B have number of sides in the ratio 1 : 2 and interior angles in the ratio 3 : 4. Then the number of sides of B equals

Accepted Answer

Let the number of sides of polygons A and B be n and 2n, respectively.

$\frac{(n - 2)180}{n} \div \frac{(2n - 2)180}{2n} = \frac{3}{4}$

$\frac{n - 2}{n - 1} = \frac{3}{4}$

$4n - 8 = 3n - 3$

n = 5

The Number of sides of polygon B is 2*5 = 10

Question 3.