CAT 2022 Slot 2 QA Question 4: 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

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.

The interior angle of a regular polygon with $s$ sides is:

$\dfrac{{(s - 2) 	imes 180}}{s}$

Using the given ratio of interior angles:

$\dfrac{\dfrac{{(n - 2) 	imes 180}}{n}}{\dfrac{{(2n - 2) 	imes 180}}{{2n}}} = \dfrac{