Question

Let A and B be two regular polygons having a and b sides, respectively. If b = 2a and each interior angle of B is $\frac{3}{2}$ times each interior angle of A, then each interior angle, in degrees, of a regular polygon with a + b sides is

• A. 120
• B. 150
• C. 160
• D. 130

Answer 1

Answer: (B)

150

Answer 2

The formula for the interior angle of a regular polygon is given by $180−\frac{360}{n}$​, where ‘$n$’ represents the number of sides.

$⇒180−\frac{360}{2a}​=\frac{3}{2}​(180−360a)$

$⇒360−360a=540−3×360a$

$⇒2×360a=180$

$⇒a=\frac{2×360}{180}​$

$⇒a=4$ and $b=2a=8$

Therefore, a polygon with each side equal to $a+b=4+8=12$ will have each interior angle equal to $180−\frac{360}{12}=150.$