document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=705592>Question 705592</A>: <I><SPAN STYLE=\"word-break: break-all;\"> if the sum of the measure of the angles of a apolygon is 2340 how many diagonals does it have?<BR>\n" );
document.write( "how do you do this problem... </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #434707 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39630)</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=434707\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> This is a (regular) polygon of 15 sides.  If you wanted to, you could literally draw this on  paper, and individually draw and count all of the diagonals.  The harder way is to do this for just the first simpler regular polygons and try to develop a formula, and then use it to compute the number of diagonals for a polygon of 15 sides.  \r<BR>\n" );
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document.write( "You can figure the number of sides using 180*(n-2) being the sum of the interior angles of a regular polygon (which you can find by using any polygon cut into separate triangles cutting at exactly one vertex.\r<BR>\n" );
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document.write( "This was difficult to analyze but it seems to give me something that may work.\r<BR>\n" );
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document.write( "___n_________diagonals<BR>\n" );
document.write( "___3_________0<BR>\n" );
document.write( "___4_________2<BR>\n" );
document.write( "___5_________5<BR>\n" );
document.write( "___6_________9<BR>\n" );
document.write( "___7_________14\r<BR>\n" );
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document.write( "There seems to be a (n-3) happenig.  <BR>\n" );
document.write( "Adjusting the n=4, the n-3 give a 1, and so 4/2=2.<BR>\n" );
document.write( "At n=5, the n-3 gives 2, so to get 5 diags, I tried 5/2 times this n-3.<BR>\n" );
document.write( "I believe but not yet sure, that n(n-3)/2  may give the number of diagonals in a polygon of n sides.  \r<BR>\n" );
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document.write( "Just to keep checking, will this formula give me 14 when n=7?<BR>\n" );
document.write( "7(7-3)/2=7(4)/2=7(2)=14, okay here.<BR>\n" );
document.write( "What about n=6?<BR>\n" );
document.write( "6(6-3)/2=6(3)/2=3*3=9, okay here too. \r<BR>\n" );
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document.write( "To be more certain, maybe a proof my mathematical induction? </SPAN>\n" );
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