document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1191938>Question 1191938</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How many sides does a polygon have if the sum of its interior angles is 7 times the sum of its exterior angles?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #823810 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13198)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=823810\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "The way the problem is stated, the result has to be independent of what type of polygon it is, so we can choose the special case where the polygon is regular.<br><BR>\n" );
document.write( "Then, if the sum of the interior angles is 7 times the sum of the exterior angles, then the measure of one interior angle is 7 times the measure of one exterior angle.<br><BR>\n" );
document.write( "x = exterior angle<BR>\n" );
document.write( "7x = interior angle<br><BR>\n" );
document.write( "The sum of the measures of an interior angle and an exterior angle is 180 degrees:<br><BR>\n" );
document.write( "x+7x=180<BR>\n" );
document.write( "8x=180<BR>\n" );
document.write( "x=180/8=22.5<br><BR>\n" );
document.write( "The measure of an exterior angle of a regular polygon is 360 degrees, divided by the number of sides.<br><BR>\n" );
document.write( "360/n=22.5<BR>\n" );
document.write( "n=360/22.5=16<br><BR>\n" );
document.write( "ANSWER: 16 sides<br><BR>\n" );
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