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

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. ( n − 2 ) 180 n ( 2 n − 2 ) 180 2 n = 3 4 \ \dfrac{\ \ \dfrac{\ \left(n-2\right)180}{n}}{\ \dfrac{\ \left(2n-2\right)180}{2n}}=\dfrac{3}{4} 2 n ( 2 n − 2 ) 180 ​ n ( n − 2 ) 180 ​ ​ = 4 3 ​ n − 2 n − 1 = 3 4 \ \dfrac{\ \ \ n-2}{\