Question

How many sides does a regular polygon have if each of its interior angles is ${165}^{\circ }$?

Answer 1

Measure of each interior angle $={165}^{\circ }$
So, measure of each exterior angle $={180}^{\circ }-{165}^{\circ }={15}^{\circ }$

Sum of exterior angles of any polygon $={360}^{\circ }$

So, number of sides $=\frac{360}{15}=24$

Hence, the polygon has $24$ sides.