Question

How many sides does a regular polygon have if each of its interior angles is $165°$?

Answer 1

Using exterior angle property of polygons to find the number of sides:

It is known that the measure of each interior angle is $165°$.

Then, each exterior angle $=180°-165°$ [$\because$exterior angle = $180°-$ interior angle]

$\Rightarrow$ $=15°$

$\because$ (number of sides) $\times$ (the measure of each exterior angle) $=360°$ [Using exterior angle property of polygons]

$\Rightarrow$ (number of sides) $\times 15°=360°$

$\Rightarrow$ Number of sides $=\frac{360°}{15°}$

$\Rightarrow$ $=24$

Therefore, a polygon with interior angles $165°$ has $24$ sides.