document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=768150>Question 768150</A>: <I><SPAN STYLE=\"word-break: break-all;\"> if doubling the number of sides of a regular polygon increase the angle between adjacent sides by 10 degrees, what is the original 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 #468140 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39617)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=468140\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You could find that calculating the interior angle at each vertex, you would be using equivalent to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=180-360%2Fn ALIGN=MIDDLE  ALT=\"180-360%2Fn\"   DISABLED_style= \"max-width:90%; height:auto;\" >, which could also be used as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=180%281-2%2Fn%29 ALIGN=MIDDLE  ALT=\"180%281-2%2Fn%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > for the degrees of each interior angle, at a vertex, n being the number of sides in the polygon.\r<BR>\n" );
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document.write( "Now, n is an unknown variable.\r<BR>\n" );
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document.write( "Doubled number of sides, vertex angle 180(1-2/(2n)) degrees.<BR>\n" );
document.write( "Original number of sides, vertex angle (180-2/n).\r<BR>\n" );
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document.write( "Their difference is 10 degrees:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28180%2A%281-2%2F%282n%29%29-180%281-2%2Fn%29=10%29 ALIGN=MIDDLE  ALT=\"highlight%28180%2A%281-2%2F%282n%29%29-180%281-2%2Fn%29=10%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=180-180%2Fn-180%2B360%2Fn=10 ALIGN=MIDDLE  ALT=\"180-180%2Fn-180%2B360%2Fn=10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-180%2B360=10n ALIGN=MIDDLE  ALT=\"-180%2B360=10n\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=180=10n ALIGN=MIDDLE  ALT=\"180=10n\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28n=18%29 ALIGN=MIDDLE  ALT=\"highlight%28n=18%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > original sides, to be doubled, giving 10 degree increase at each vertex. </SPAN>\n" );
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