Question 740778
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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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<pre>
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(n-2)}}} - - - it is one of the basic facts of Geometry.


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

    {{{2pi}}} = {{{pi(n-2)}}}.


Cancel  {{{pi}}}  in both sides

    2 = n - 2.


Get  n = 2 + 2 = 4.


<U>ANSWER</U>.  n = 4:  an n-gon is a quadrilateral.
</pre>

Solved.