Question

If an angle of a regular polygon is ${165}^0$,then the number of sides of the polygon is

• A. $30$
• B. $24$
• C. $18$
• D. $15$

Answer 1

The correct option is B $24$

Given : An angle of a regular polygon is ${165}^o$

Let $n$ denote the number of sides of s polygon

By using the formula

An angle of a polygon $=\frac{(n-2)180}{n}$

$⟹$ $165=\frac{(n-2)180}{n}$

$⟹$ $165n=180n-360$

$⟹$ $25n=360$

$\therefore n=24$

$\therefore$ number of sides of the polygon is $24$.