Question

Question 4
How many sides does a regular polygon have if each of its interior angles 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 $={360}^{\circ }$
Hence, the number of sides
$=\frac{Sumofexteriorangles}{Eachexteriorangle}=\frac{{360}^{\circ }}{15}=24$
Hence, the regular polygon has 24 sides.