document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=178210>Question 178210</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In each of the following, determine the number of sides of<BR>\n" );
document.write( "a regular polygon with the stated property. If such a regular<BR>\n" );
document.write( "polygon does not exist, explain why.<BR>\n" );
document.write( "Each exterior angle measures 25°.<BR>\n" );
document.write( "The total number of diagonals is 4860. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #133172 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=133172\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> In each of the following, determine the number of sides of<BR>\n" );
document.write( "a regular polygon with the stated property. If such a regular<BR>\n" );
document.write( "polygon does not exist, explain why.<BR>\n" );
document.write( "-----------\r<BR>\n" );
document.write( "\n" );
document.write( "1. Each exterior angle measures 25°.<BR>\n" );
document.write( "The sum of the exterior angles is 360<BR>\n" );
document.write( "number of sides= 360/25 = 14.4<BR>\n" );
document.write( "That doesn't make any sense.<BR>\n" );
document.write( "------------------------------------\r<BR>\n" );
document.write( "\n" );
document.write( "The total number of diagonals is 4860.<BR>\n" );
document.write( "nC2 - n is the number of diagonals of a regular polygon with n sides<BR>\n" );
document.write( "nC2 - n = [n(n-1)]/[1*2] - n = (n^2-n)/2 - n<BR>\n" );
document.write( "--------<BR>\n" );
document.write( "(n^2-n)/2 - n = 4860<BR>\n" );
document.write( "n^2 - n -2n = 9720<BR>\n" );
document.write( "n^2 - 3n - 9720 = 0<BR>\n" );
document.write( "solve for n<BR>\n" );
document.write( "==============<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );