Question 1107580: THE INTERIOR ANGLE ME A REGULAR CONVEX POLYGON IS 156 . HOW MANY SIDES HAS THE POLYGON? Found 2 solutions by ikleyn, Alan3354:Answer by ikleyn(52787) (Show Source):
You can express the sum of all interior angle of any convex polygon with n sides (n vetices) as 180°*(n-2).
From the other side, the sum of all interior angle of any regular polygon is , where is any of its interioir angle.
Thus you have this equation
180*(n-2) = n*156.
where n is unknown number of sides (of vertices). Simplify and solve for n:
180n - 360 = 156n ====> 180n - 156n = 360 ====> 24n = 360 ====> n = = 15.
Answer. 15 sides and/or 15 verices.
You can put this solution on YOUR website! THE INTERIOR ANGLE ME A REGULAR CONVEX POLYGON IS 156 . HOW MANY SIDES HAS THE POLYGON?
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Ext angles = 180-156 = 24 degs
360/24 = 15 sides
