document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=937379>Question 937379</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If the difference in the degree measure of interior and exterior angle of a regular polygon is 100, how many sides does it have? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #570872 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=570872\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> if x is the interior angle, then 180 - x is the exterior angle.\r<BR>\n" );
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document.write( "you get:\r<BR>\n" );
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document.write( "x + (180 - x) = 180\r<BR>\n" );
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document.write( "if the difference between them is equal to 100, then you get:\r<BR>\n" );
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document.write( "x - (180 - x) = 100\r<BR>\n" );
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document.write( "simplify this to get:\r<BR>\n" );
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document.write( "x - 180 + x = 100\r<BR>\n" );
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document.write( "combine like terms to get:\r<BR>\n" );
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document.write( "2x - 180 = 100\r<BR>\n" );
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document.write( "add 180 to both sides to get:\r<BR>\n" );
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document.write( "2x = 280\r<BR>\n" );
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document.write( "divide both sides by 2 to get:\r<BR>\n" );
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document.write( "x = 140.\r<BR>\n" );
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document.write( "the formula for the interior angle of a regular polygon is a = 180 * (n-2) / n.\r<BR>\n" );
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document.write( "if the interior angle is 140, then the formula becomes:\r<BR>\n" );
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document.write( "140 = 180 * (n-2) / n\r<BR>\n" );
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document.write( "multiply both sides by n to get:\r<BR>\n" );
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document.write( "140 * n = 180 * (n - 2)\r<BR>\n" );
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document.write( "simplify to get:\r<BR>\n" );
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document.write( "140 * n = 180 * n - 360\r<BR>\n" );
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document.write( "add 360 to both sides to get:\r<BR>\n" );
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document.write( "140 * n + 360 = 180 * n\r<BR>\n" );
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document.write( "subtract 140 * n from both sides to get:\r<BR>\n" );
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document.write( "360 = 180 * n - 140 * n\r<BR>\n" );
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document.write( "simplify to get:\r<BR>\n" );
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document.write( "360 = 40 * n\r<BR>\n" );
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document.write( "divide both sides by 40 to get:\r<BR>\n" );
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document.write( "360 / 40 = n\r<BR>\n" );
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document.write( "solve for n to get:\r<BR>\n" );
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document.write( "n = 9.\r<BR>\n" );
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document.write( "you can derive the number of sides by use of the external angle as well.\r<BR>\n" );
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document.write( "the formula for the number of sides from the external angle is much simpler.\r<BR>\n" );
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document.write( "the sum of the external angles of a polygon is always 360, so the number of sides will be 360 / the external angle.\r<BR>\n" );
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document.write( "if the internal angle is 140, then the external angle is 180 - 140 = 40.\r<BR>\n" );
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document.write( "360 / 40 = 9.\r<BR>\n" );
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document.write( "same answer but much simpler to calculate.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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