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How many sides does a regular polygon have if each of its interior angles is 165°?

4. How many sides does a regular polygon have if each of its interior angles is 165°?

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 The measure of each interior angle is 165°

So, measure of each exterior angle = 180°-165° = 15°

Regular polygon has all exterior angles equal.

Let number of sides of polygon = n

Sum of Exterior angles of a polygon = 360\degree

                                                                                 \left ( n \right )\ast 15\degree= 360\degree

                                                                                       n = 24

Hence,regular polygon having each of its interior angles is 165° has 24 sides.

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