document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1133816>Question 1133816</A>: <I><SPAN STYLE=\"word-break: break-all;\"> solve a regular polygon of (2x+1) sides has 140 as the size of each interior angle, find x. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #751067 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=751067\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> if the internal angle is 140, then the external angle is 180 - 140 = 40 degrees.\r<BR>\n" );
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document.write( "the number of sides is therefore 360 / 40 = 9 because 9 * 40 = 360.\r<BR>\n" );
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document.write( "therefore 2x + 1 = 9<BR>\n" );
document.write( "subtract 1 from both sides to get 2x = 8<BR>\n" );
document.write( "divide both sides by 2 to get x = 4.\r<BR>\n" );
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document.write( "your solution is x = 4.\r<BR>\n" );
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document.write( "the number of sides can also be obtained from the internal angle.\r<BR>\n" );
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document.write( "the formula for that is i = 180 * (n - 2) / n\r<BR>\n" );
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document.write( "i is the internal angle.<BR>\n" );
document.write( "n is the number of sides.\r<BR>\n" );
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document.write( "to solve this equation for n, do the following.\r<BR>\n" );
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document.write( "multiply both sides of the equation by n to get i * n = 180 * (n - 2)\r<BR>\n" );
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document.write( "simplify to get i * n = 180 * n - 360\r<BR>\n" );
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document.write( "subtract i * n from both sides of the equation and add 360 to both sides of the equation to get 360 = 180 * n - i * n\r<BR>\n" );
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document.write( "factor out the n to get 360 = n * (180 - i)\r<BR>\n" );
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document.write( "divide both sides of the equation by n * (180 - i) to get:\r<BR>\n" );
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document.write( "360 / (180 - i) = n\r<BR>\n" );
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document.write( "since i = 140, this becomes 360 / (180 - 140) = n which becomes 360 / 40 = n which becomes 9 = n.\r<BR>\n" );
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document.write( "it's much easier to use the external angle if you can find it.\r<BR>\n" );
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document.write( "the external angle is always 180 - the internal angle.\r<BR>\n" );
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document.write( "in this case the external angle was 180 - 140 = 40.\r<BR>\n" );
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document.write( "the answer is the same as when using the internal angle directly, just easier to derive.\r<BR>\n" );
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document.write( "2x + 1 = 9<BR>\n" );
document.write( "solve for x to get x = 4.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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