Question

The interior angles of a regular polygon are each ${165}^o$. How many sides does the polygon have?

• A. 17
• B. 20
• C. 22
• D. 24
• E. 28

Answer 1

The correct option is D 24

If the number of sides of a regular polygon is $n$ , then the interior angles of regular polygon is $\frac{(n-2)\left(180\right)}{n}$
Given that interior angle is $165$.
So we get $\frac{(n-2)}{n}=\frac{165}{180}=\frac{11}{12}$ , which implies $12n-11n=24$
Therefore, the value of $n$ is $24$ , which implies that there are $24$ sides for a regular polygon with interior angles $165$.