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If the measure of each interior angle of a regular polygon is 165, find the number of sides of the polygon.

If the measure of each interior angle of a regular polygon is 165, find the number of sides of the polygon.
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If the measure of each interior angle of a regular polygon is 165, find the number of sides of the polygon.

User Ekta Padaliya
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2 Answers

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There is an equation for this. You take 180°-165°=15°. Then you take 360÷15=24. So there are 24 exterier angles with each angle being 15°. Since there are 24 exterior angles, there are 24 sides.
User Thijs Koerselman
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If the interior angle of a regular polygon is 165°, then the size of its exterior angle is 15°. Since the exterior angles of a polygon always add to 360°, then the number of sides is 360/15 = 24.

There are 24 sides on this polygon. Answer is 24
User Arthur Pereira
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8.5k points
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