document.write( "Question 632046: can you please show to me the proof of the sum of the exterior angles of any polygons which is equal to 720 degrees..thank you. \n" ); document.write( "
Algebra.Com's Answer #397968 by Theo(13342)\"\" \"About 
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The sum of the exterior angles of a polygon is equal to 360 degrees (not 720).
\n" ); document.write( "let I = the interior angle of a polygon.
\n" ); document.write( "let E = the exterior angle of a polygon.
\n" ); document.write( "The exterior angle of a polygon is equal to 180 - the interior angle of a polygon.
\n" ); document.write( "This is expressed as:
\n" ); document.write( "E = 180 - I
\n" ); document.write( "The sum of the interior angles of a polygon is given by the formula:
\n" ); document.write( "sum(I) = (n-2)*180 where n is the number of sides of the polygon.
\n" ); document.write( "From this formula, the interior angle of a formula is calculated as:
\n" ); document.write( "I = (n-2)*180/n
\n" ); document.write( "Since the exterior angle of a polygon is always supplementary to the interior angle of a polygon, this means that:
\n" ); document.write( "E = 180 - (n-2)*180/n
\n" ); document.write( "simplify this formula to get:
\n" ); document.write( "E = 180 - (180n-360)/n
\n" ); document.write( "Since 180 = 180n/n, this equation can be rewritten as:
\n" ); document.write( "E = 180n/n - (180n-360)/n
\n" ); document.write( "This can be further simplified to:
\n" ); document.write( "E = 180n/n - 180n/n + 360/n
\n" ); document.write( "Combine like terms and you get:
\n" ); document.write( "E = 360/n
\n" ); document.write( "Multiply both sides of this equation by n to get:
\n" ); document.write( "n*E = 360
\n" ); document.write( "Since n*E is equal to the sum of the exterior angles of any polygon, this means that:
\n" ); document.write( "The sum of the exterior angles of any polygon is equal to 360 degrees.\r
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