document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=236995>Question 236995</A>: <I><SPAN STYLE=\"word-break: break-all;\"> the polygon angle-sum theorem states: the sum of the measures of the angles of an n-gon is____ ?\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #174330 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=174330\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the sum of the INTERIOR angles of a polygon is equal to (n-2) * 180 where n is equal to the number of sides.\r<BR>\n" );
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document.write( "sum of the interior angles of a triangle = 3 sides = (3-2) * 180 = 180\r<BR>\n" );
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document.write( "sum of the interior angles of a quadrilateral = 4 sides = (4-2) * 180 = 360 degrees.\r<BR>\n" );
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document.write( "the sum of the EXTERIOR angles of a polygon is always equal to 360 degrees.\r<BR>\n" );
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document.write( "The exterior angle of a polygon is equal to the supplement of the interior angle of a polygon.\r<BR>\n" );
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document.write( "each interior angle of a regular polygon is equal to the sum of the angles divided by the number of sides.\r<BR>\n" );
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document.write( "for a regular triangle, each interior angle is equal to 180/3 = 45.\r<BR>\n" );
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document.write( "for a regular quadrilateral, each interior angle is equal to 360/4 = 90 degrees.\r<BR>\n" );
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document.write( "a regular polygon has each interior angle equal to each other.\r<BR>\n" );
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document.write( "for a regular triangle, each interior angle = 60 degrees and each exterior angle = 180-60 = 120 degrees.   sum of exterior angles is equal to 3 * 120 = 360.\r<BR>\n" );
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document.write( "for a regular quadrilateral (square / rectangle) each exterior angle = 180 - 90 = 90 degrees.  sum of exterior angles is equal to 4 * 90 = 360.\r<BR>\n" );
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document.write( "this works for all polygons up to n sides.\r<BR>\n" );
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document.write( "for a pentagon, sum of interior angles = (5-2) * 180 = 540 degrees.   each interior angle = 540 / 5 = 108 degrees.\r<BR>\n" );
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document.write( "each exterior angle  = (180-108) = 72 degrees.   sum of exterior angles = 5 * 72 degrees = 360 degrees.\r<BR>\n" );
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