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A polygon has each exterior angle equal to 30 degrees. How many sides does it have ?

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carry1 | Student | (Level 2) eNoter

Posted March 6, 2011 at 3:07 AM via web

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A polygon has each exterior angle equal to 30 degrees. How many sides does it have ?

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted March 6, 2011 at 3:12 AM (Answer #1)

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We use the property that the sum of all the angles of a polygon with n sides is equal to 180*(n - 2).

If the exterior angles are equal to 30 degrees, the interior angles are equal to 180 - 30 = 150 degrees.

If there are n-sides in the polygon, the sum of all n angles would be equal to 150*n

Equating 150*n = 180*(n - 2)

=> 150n = 180n - 360

=> 30n = 360

=> n = 360/30

=> n = 12

The polygon has 12 sides.

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