document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=250513>Question 250513</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the number of sides in a regular polygon if:<BR>\n" );
document.write( "the measure of an interior angle exceeds 6 times the measure of an exterior angle by 12 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #182413 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=182413\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> i = measure of the interior angle of regular polygon.<BR>\n" );
document.write( "e = measure of the exterior angle of regular polygon.\r<BR>\n" );
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document.write( "i = 6*e + 12\r<BR>\n" );
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document.write( "s = number of sides in regular polygon.\r<BR>\n" );
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document.write( "exterior angle = 360 divided by number of sides = 360/s\r<BR>\n" );
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document.write( "interior angle = (s-2)*180 / s\r<BR>\n" );
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document.write( "example:\r<BR>\n" );
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document.write( "exterior angle of regular triangle = 360 / 3 = 120\r<BR>\n" );
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document.write( "interior angle of regular triangle = 1*180/3 = 60\r<BR>\n" );
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document.write( "the interior angle of a polygon and its associated exterior angle are supplementary to each other.  the sum of their angles is 180.\r<BR>\n" );
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document.write( "we get i + e = 180\r<BR>\n" );
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document.write( "we also get:\r<BR>\n" );
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document.write( "i = 6*e + 12\r<BR>\n" );
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document.write( "substitute in supplementary equation to get:\r<BR>\n" );
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document.write( "6*e + 12  + e = 180\r<BR>\n" );
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document.write( "combine like terms to get:\r<BR>\n" );
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document.write( "7*e + 12 = 180\r<BR>\n" );
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document.write( "subtract 12 from both sides of equation to get:\r<BR>\n" );
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document.write( "7*e = 180 - 12 = 168\r<BR>\n" );
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document.write( "divide both sides of equation by 7 to get:\r<BR>\n" );
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document.write( "e = 168/7 = 24.\r<BR>\n" );
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document.write( "i = 6*24 + 12 = 156\r<BR>\n" );
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document.write( "156 + 24 = 180 so the angles are supplementary as they should be.\r<BR>\n" );
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document.write( "we have:\r<BR>\n" );
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document.write( "i = 156<BR>\n" );
document.write( "e = 24\r<BR>\n" );
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document.write( "formula for exterior angle of a regular polygon is:\r<BR>\n" );
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document.write( "e = 360/s\r<BR>\n" );
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document.write( "this becomes\r<BR>\n" );
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document.write( "24 = 360/s\r<BR>\n" );
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document.write( "solve for s to get:\r<BR>\n" );
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document.write( "s = 15\r<BR>\n" );
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document.write( "number of sides in the regular polygon appears to be 15.\r<BR>\n" );
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document.write( "substitute in equation for interior angle of polygon to get:\r<BR>\n" );
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document.write( "156 = (s-2)*180/s\r<BR>\n" );
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document.write( "solve for s.\r<BR>\n" );
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document.write( "mulltiply both sides of the equation by s to get:\r<BR>\n" );
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document.write( "156*s = (s-2)*180\r<BR>\n" );
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document.write( "simplify by removing parentheses to get:\r<BR>\n" );
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document.write( "156*s = 180*s - 360\r<BR>\n" );
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document.write( "solve for s to get:\r<BR>\n" );
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document.write( "24*s = 360\r<BR>\n" );
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document.write( "s = 360/24 = 15\r<BR>\n" );
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document.write( "everything checks out so the answer is:\r<BR>\n" );
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document.write( "number of sides of the regular polygon is 15.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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