Question

how many sides does a regular polygon have if the each of the interior angles is 165​

Answer 1

Here is an easy way to solve the problem:

1) The interior and the exterior angles

make a linear pair: add up to make 180°.

180° - 165° = 15° measure of one ext. angle

2) the sum of the exterior angles of any convex polygon is 360°

360° ÷ 15° = 24 exterior angles

3) the number of exterior angles = the number of interior angles = the number of sides in any convex polygon

4) Therefor there are 24 sides in this regular polygon

Answer 2

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Ingerior angle = 165

Exterior angle = 180 - 165 = 15

Ingerior angle = The sum of exterior angles of any polygon is 360

Ingerior angle = 165Exterior angle = 180 - 165 = 15.

Number of sides = 360/15 = 24......

☠️Hope it helps you☠️