document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1095670>Question 1095670</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The ratio between an exterior and interior angle is1:8.Find the number of sides </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #710207 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=710207\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the exterior angle and the interior angle are supplementary to each other.\r<BR>\n" );
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document.write( "this means that their sum is 180 degrees.\r<BR>\n" );
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document.write( "let i = the interior angle and let e equal the exterior angle.\r<BR>\n" );
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document.write( "therefore i + e = 180\r<BR>\n" );
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document.write( "the ratio between them is 1/8, therefore e/i = 1/8.\r<BR>\n" );
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document.write( "solve for e to get e = 1/8 * i\r<BR>\n" );
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document.write( "i + e = 180 becomes i + 1/8 * i = 180\r<BR>\n" );
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document.write( "multiply both sides of this equation by 8 to get 8i + i = 8 * 180\r<BR>\n" );
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document.write( "combine like terms to get 9i = 8 * 180\r<BR>\n" );
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document.write( "divide both sides of this equation by 9 to get i = 8 * 20\r<BR>\n" );
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document.write( "solve for i to get i = 160 degrees.\r<BR>\n" );
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document.write( "this makes e equal to 180 - 160 = 20 degrees.\r<BR>\n" );
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document.write( "the number of sides of a polygon can be found by use of the following formula.\r<BR>\n" );
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document.write( "n = 360 / e\r<BR>\n" );
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document.write( "n = number of sides<BR>\n" );
document.write( "e = the exterior angle in degrees.\r<BR>\n" );
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document.write( "if you know i, you can find e by using the formula of e = 180 - i.\r<BR>\n" );
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document.write( "i = the interior angle in degrees.\r<BR>\n" );
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document.write( "we found i and from that found e and from that found the number of sides of the polygon.\r<BR>\n" );
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document.write( "in the equation of e/i = 1/8, we could have solve for e directly to get:\r<BR>\n" );
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document.write( "i = 8 * e\r<BR>\n" );
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document.write( "then i + e = 180 becomes 8 * e + e = 180 which becomes 9 * e = 180 which results in e = 20 degrees.\r<BR>\n" );
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document.write( "either way we derived e = 20 degrees and from that were able to derive that the number of sides of the polygon is equal to 360 / e = 360 / 20 = 18.\r<BR>\n" );
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document.write( "note that the ratio had to be e/i = 1/8 and could not be i/e = 1/8\r<BR>\n" );
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document.write( "if i/e = 1/8, then we solve for e to get e = 8 * i\r<BR>\n" );
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document.write( "from that we get i + e = 180 becomes i + 8 * i = 180 which results in 9*i = 180 which results in i = 20.\r<BR>\n" );
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document.write( "this makes e = 160 and the number of sides equal to 360 / 160 = 2.25 which can't be because the number of side has to be an integer.\r<BR>\n" );
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document.write( "the ration had to be e/i = 1/8.\r<BR>\n" );
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document.write( "alternatively i/e = 8 would have worked as well.\r<BR>\n" );
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document.write( "both would get you i = 8 * e.\r<BR>\n" );
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document.write( "your solution is that the number of sides of the polygon is 18.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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