SOLUTION: THE INTERIOR ANGLE ME A REGULAR CONVEX POLYGON IS 156 . HOW MANY SIDES HAS THE POLYGON?

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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 put this solution on YOUR website!
.
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.

Solved.


Answer by Alan3354(69443)   (Show Source): 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
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