Question

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

Answer 1

Let number of sides be n.
Exterior angle $={180}^{\circ }-{165}^{\circ }={15}^{\circ }$
Sum of exterior angles of a regular polygon $={360}^{\circ }$
Number of sides $=\frac{\text{Sum of exterior angles}}{\text{Each exterior angles}}=\frac{{360}^{\circ }}{{15}^{\circ }}=24$
Hence, the regular polygon has 24 sides.