document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=966906>Question 966906</A>: <I><SPAN STYLE=\"word-break: break-all;\">  the ratio of the interior angle of the exterior angle of a regular polygon is 5:2.find the number of sides of the polygon.google.com </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #590988 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=590988\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the exterior angle of a regular polygon is equal to 360 / n, where nis the number of sides.\r<BR>\n" );
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document.write( "the interior angle of a regular polygon is equal to 180 - 360 / n, where n is the number of sides.\r<BR>\n" );
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document.write( "the ratio of the interior angle of the polygon to the exterior angle of the polygon is equual to 5/2.\r<BR>\n" );
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document.write( "thie means that (180 - 360 / n) / (360 / n) is equal to 5 / 2.\r<BR>\n" );
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document.write( "take the cross product to get:\r<BR>\n" );
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document.write( "5 * (360 / n) is equal to 2 * (180 - 360 / n)\r<BR>\n" );
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document.write( "solve for n to get n = 7.\r<BR>\n" );
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document.write( "when n = 7, the exereior angle is 360 / 7 = 51.42857143 degrees.\r<BR>\n" );
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document.write( "when n = 7, the interior angle is 180 - 51.42857143 degrees which is equal to 128.5714286 degrees.\r<BR>\n" );
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document.write( "the ratio of the interior angle to the exterior angle is equal to 128.5714286 / 51.42857143 which is equal to 2.5.\r<BR>\n" );
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document.write( "Multiply the numerator and denominator of 2.5 / 1 to get 5 / 2.\r<BR>\n" );
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document.write( "the solution is confirmed as good.\r<BR>\n" );
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document.write( "another calculation for the interioa angle would be (n-2) * 180 / n.\r<BR>\n" );
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document.write( "when n = 7, that becomes 5 * 180 / 7 which becomes 128.5714286.\r<BR>\n" );
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document.write( "the interior angle can be calculated in both ways.\r<BR>\n" );
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document.write( "it's the same either way.<BR>\n" );
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