Cullen Banks

2023-03-02

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

Shanty4xr

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

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