SOLUTION: How Many Sides Are In The Polygon If The Measure Of The Interior Angle Is 156?

Question 565065: How Many Sides Are In The Polygon If The Measure Of The Interior Angle Is 156?
Found 2 solutions by Alan3354, kingme18:
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
How Many Sides Are In The Polygon If The Measure Of The Interior Angle Is 156?
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Ext angles = 180 - 156 = 24 degs
360/24 = 15 sides

Answer by kingme18(98) (Show Source): You can put this solution on YOUR website!
Assuming that this is a regular polygon...
The easiest way to do this is to recall that the sum of the EXTERIOR angles is 360, and that an interior angle + its exterior angle = 180 (because they make a straight line). Thus, if the interior angles are each 156, the exterior angles are each 180-156=24. Now, if you take 360/24 (because each exterior angle is 24 and they need to add to 360), you get 15. Thus, there are 15 sides.
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