document.write( "Question 215232: The measure of each interior angle of a regular polygon is 11 times that of the exterior angle. How many sides does the polygon have?\r
\n" ); document.write( "\n" ); document.write( "I can solve this one by using the chart our teacher had us make, that calculates interior and exterior angles for several regular polygons. But is there also a mathematical way of solving this question?\r
\n" ); document.write( "\n" ); document.write( "Please explain.
\n" ); document.write( "Thank you!\r
\n" ); document.write( "\n" ); document.write( "Saskia \n" ); document.write( "
Algebra.Com's Answer #162646 by Alan3354(69443)\"\" \"About 
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The measure of each interior angle of a regular polygon is 11 times that of the exterior angle. How many sides does the polygon have?
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\n" ); document.write( "First find the interior angle.
\n" ); document.write( "The interior and exterior are supplementary, meaning they total 180 degs.
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\n" ); document.write( "I = 11*E
\n" ); document.write( "I + E = 180
\n" ); document.write( "11E + E = 180
\n" ); document.write( "E = 15 degs
\n" ); document.write( "I = 165 degs
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\n" ); document.write( "Then, the total of all interior angles of a polygon is 180*(n-2) where n is the # of sides and angles.
\n" ); document.write( "I = Total of angles/# of angles
\n" ); document.write( "I = 180*(n-2)/n = 165
\n" ); document.write( "165n = 180n - 360
\n" ); document.write( "-15n = -360
\n" ); document.write( "n = 24
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