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