Question

How many sides does a regular polygon have if each of its interior angles is ${165}^{\circ }$? (2 marks)

Answer 1

Let number of sides be n. (0.5 marks)
Exterior angle $={180}^{\circ }-{165}^{\circ }={15}^{\circ }$ (0.5 marks)
Sum of exterior angles of a regular polygon $={360}^{\circ }$ (0.5 marks)
Hence, the number of sides
$=\frac{Sumofexteriorangles}{Eachexteriorangle}=\frac{{360}^{\circ }}{15}=24$
Hence, the regular polygon has 24 sides. (1 mark)