document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=478149>Question 478149</A>: <I><SPAN STYLE=\"word-break: break-all;\"> please help me solve this question: each interior angle of a regular polygon is four times the measure of each exterior angle. how many diagonals does the polygon have?<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #327622 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=327622\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> each interior angle is equal to 4 times the exterior angle.<BR>\n" );
document.write( "ia = interior angle<BR>\n" );
document.write( "ea = exterior angle<BR>\n" );
document.write( "ie ea = x then ia = 4x<BR>\n" );
document.write( "now the interior angle of a polygon and its exterior angle are supplementary.<BR>\n" );
document.write( "this means that ia + ea = 180<BR>\n" );
document.write( "this means that 4x + x = 180 which means that 5x = 180 which means that x = 36 degrees which means that 4x = 144 degrees.<BR>\n" );
document.write( "ea = 36 degrees<BR>\n" );
document.write( "ia = 144 degrees<BR>\n" );
document.write( "now the sum of the exterior angles of a polygon is always equal to 360 degrees.<BR>\n" );
document.write( "if you divide 360 by 36 you get 10.<BR>\n" );
document.write( "this means that the polygon has 10 sides.<BR>\n" );
document.write( "it's a decagon.<BR>\n" );
document.write( "so far so good.<BR>\n" );
document.write( "now you want to determine how many diagonals the decagon has.<BR>\n" );
document.write( "the formula for determining the number of diagonals in a polygon is:<BR>\n" );
document.write( "d = n(n-3)/2<BR>\n" );
document.write( "d is the number of diagonals<BR>\n" );
document.write( "n is the number of sides.<BR>\n" );
document.write( "if it's a triangle, then the number of diagonals is equal to 3*0/2 = 0<BR>\n" );
document.write( "if it's a quadrilateral, then the number of diagonals is 4*1/2 = 2<BR>\n" );
document.write( "pentagon = 5*2/2 = 5<BR>\n" );
document.write( "hexagon = 6*3/2 = 9<BR>\n" );
document.write( "septagon = 7*4/2 = 14<BR>\n" );
document.write( "octagon = 8*5/2 = 20<BR>\n" );
document.write( "nonagon or enneagon (9 sides) = 9*6/2 = 27<BR>\n" );
document.write( "decagon = 10*7/2 = 35<BR>\n" );
document.write( "the decagon will have 35 diagonals.<BR>\n" );
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