SOLUTION: If the measure of the interior angle is 150 degrees of a regualr polygon, how many sides does it have?

Question 1130259: If the measure of the interior angle is 150 degrees of a regualr polygon, how many sides does it have?
Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39614) (Show Source): You can put this solution on YOUR website!
n sides

Answer by greenestamps(13195) (Show Source): You can put this solution on YOUR website!

Using the formula for the measure of an interior angle of a regular polygon is certainly valid.

But the formula for the measure of an exterior angle of a regular polygon is much easier to work with, so you will get to the answer to the problem faster and with less effort using it.

If the interior angle is 150 degrees, the exterior angle is 180-150 = 30 degrees. The measure of an exterior angle of a regular polygon is 360 degrees divided by the number of sides. So the number of sides is 360 degrees divided by the measure of each exterior angle: 360/30 = 12.
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