document.write( "Question 163744: This proof cannot be solved in the traditional two-column proof fashion. It has to be solved in an algebraic manner starting with an equation. Prove this theorem: One exterior angle for a regular polygon is 360/n, where n is the number of sides. Please help! \n" ); document.write( "
Algebra.Com's Answer #120621 by gonzo(654)\"\" \"About 
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prove that one exterior angle of the polygon is 360/n.
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\n" ); document.write( "sum of the interior angles of a polygon is given by the equation sum of i = (n-2)*180.
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\n" ); document.write( "since a polygon of n sides has n interior angles, then each interior angle measures ((n-2)*180)/n so the formula for an interior angle is
\n" ); document.write( "i = ((n-2)*180)/n
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\n" ); document.write( "each exterior angle is a supplement of each interior angle, so each exterior angle measure 180 - ((n-2)*180)/n) so the formula for an exterior angle is
\n" ); document.write( "e = 180 - ((n-2)*180)/n)
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\n" ); document.write( "multiplying both sides of the equation by n we get
\n" ); document.write( "n*e = n*(180-((n-2)*180)/n)
\n" ); document.write( "which becomes
\n" ); document.write( "n*e = 180*n - (180*n - 360)
\n" ); document.write( "removing parentheses this equation becomes
\n" ); document.write( "n*e = 180*n - 180*n + 360)
\n" ); document.write( "combining like terms this becomes
\n" ); document.write( "n*e = 360
\n" ); document.write( "dividing both sides of the equation by n make it
\n" ); document.write( "e = 360/n
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