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

The Correct Option is B

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 \(180−\frac{360}{12}=150.  \)