Question

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

Answer 1

Interior angle of given polygon =165°

Exterior angle of polygon

=180°−165°=15°

The sum of exterior angles of any polygon is 360°.

Number of sides of regular polygon = 360°÷15° =24°

Hence, the regular polygon with interior angle each measuring 165° is a 24-sided polygon.

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Answer 2

180°(n−2)

--------------- = 165°

n

180°(n−2) = 165°n

180°n−360°=165°n

180°n−165°n=360°

15°n=360°

n=24

Hence, the regular polygon interior angle each measuring 165 degrees is a 24-sided polygon.