SOLUTION: I have no clue as to how to answer this question! please help! If the sum of the measures of the interior angles of a convex n-gon is equal to the sum of the measures of the exter

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Question 740778: I have no clue as to how to answer this question! please help!
If the sum of the measures of the interior angles of a convex n-gon is equal to the sum of the measures of the exterior angles, how many sides does the n-gon have?
Found 3 solutions by lynnlo, Alan3354, ikleyn:
Answer by lynnlo(4176) About Me  (Show Source):
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
If the sum of the measures of the interior angles of a convex n-gon is equal to the sum of the measures of the exterior angles, how many sides does the n-gon have?
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The sum of exterior angles is always 360 degs, for all polygons.
--> what polygon has a sum of 360 degs for interior angles?

Answer by ikleyn(53570) About Me  (Show Source):
You can put this solution on YOUR website!
.
I have no clue as to how to answer this question! please help!
If the sum of the measures of the interior angles of a convex n-gon is equal
to the sum of the measures of the exterior angles, how many sides does the n-gon have?
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The sum of exterior angles of a convex n-gon is equal to  2pi,  independently on 'n'.


The sum of interior angles of a convex n-gon is equal to  pi%28n-2%29 - - - it is one of the basic facts of Geometry.


So, to answer your question, we have this equation to find  'n'

    2pi = pi%28n-2%29.


Cancel  pi  in both sides

    2 = n - 2.


Get  n = 2 + 2 = 4.


ANSWER.  n = 4:  an n-gon is a quadrilateral.

Solved.