document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1010975>Question 1010975</A>: <I><SPAN STYLE=\"word-break: break-all;\">  sum of interior angels and<BR>\n" );
document.write( "the sum of exterior angles of polygon are in<BR>\n" );
document.write( "the ratio 9:2.find the sides of regular<BR>\n" );
document.write( "polygon. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #626492 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=626492\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> ratio of the sum of the interior angles to the sum of the exterior angles is 9/2.\r<BR>\n" );
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document.write( "i believe you want to find the number of sides in the regular polygon.\r<BR>\n" );
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document.write( "the sum of the exterior angles of a polygon is always 360.\r<BR>\n" );
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document.write( "the sum of the interior angles of a polygon is equal to (n-2)*180.\r<BR>\n" );
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document.write( "since the ratio of the sum of the interior angles of the polygon to the sum of the exterior angles of the polygon is 9/2, your formula would be:\r<BR>\n" );
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document.write( "9/2 = ((n-2)*180)/360\r<BR>\n" );
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document.write( "cross multiply to get:\r<BR>\n" );
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document.write( "9 * 360 = 2 * ((n-2)*180)\r<BR>\n" );
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document.write( "simplify to get:\r<BR>\n" );
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document.write( "3240 = 2 * (180*n-360)\r<BR>\n" );
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document.write( "simplify further to get:\r<BR>\n" );
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document.write( "3240 = 360*n-720\r<BR>\n" );
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document.write( "add 720 to both sides of this equation to get:\r<BR>\n" );
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document.write( "3960 = 360*n\r<BR>\n" );
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document.write( "divide both sides of this equation by 360 to get:\r<BR>\n" );
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document.write( "n = 11\r<BR>\n" );
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document.write( "if we did this correctly, the number of sides of the regular polygon is 11.\r<BR>\n" );
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document.write( "the sum of the exterior angles is 360.\r<BR>\n" );
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document.write( "the sum of the interior angles is (11-2)*180 = 9*180 = 1620\r<BR>\n" );
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document.write( "the ratio of the sum of the interior to the sum of the exterior becomes:\r<BR>\n" );
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document.write( "1620 / 360 which is equal to 9/2 if you divide both numerator and denominator by 180.\r<BR>\n" );
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document.write( "looks good.\r<BR>\n" );
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document.write( "you can also use the cross product to see if the ratios are the same.\r<BR>\n" );
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document.write( "9/2 = 1620/360\r<BR>\n" );
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document.write( "cross multiply to get 9*360 = 2*1620 which results in 3240 = 3240 which confirms the ratios are the same.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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