Question

The sum of the interior angles of a polygon is ${1620}^{\circ }$. The number of sides of the polygon are:

• A. 9
• B. 11
• C. 15
• D. 12

Answer 1

The correct option is B 11

The sum of the interior angles of a polygon of n sides is given by the expression $(2n-4)\frac{\pi }{2}\Rightarrow (2n-4)\times \frac{\pi }{2}=1620\times \frac{\pi }{180}(2n-4)=\frac{1620\times 2}{180}=18.$
or 2n = 22
or n = 11