Cullen Banks

2023-03-02

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

Shanty4xr

Beginner2023-03-03Added 5 answers

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.

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.