document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=248366>Question 248366</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A 50-gon is a polygon with 50 sides.  How could you find the sum of the angles in a 50-gon?  What is the answer? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #181002 by </B><A HREF=/tutors/aboutme.mpl?userid=josmiceli><B>josmiceli(19441)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josmiceli><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=josmiceli><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=181002\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> First, draw lines from each vertex to some common point inside the figure<BR>\n" );
document.write( "If I start going part way around the polygon, and look only at the triangles<BR>\n" );
document.write( "formed by the lines I just drew, I add up the interior angles of each triangle.<BR>\n" );
document.write( "If the angle in the center of the 1st triangle is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A ALIGN=MIDDLE  ALT=\"A\"   DISABLED_style= \"max-width:90%; height:auto;\" >, it's angles add ip to<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=180+-+A ALIGN=MIDDLE  ALT=\"180+-+A\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and for the 2nd triangle,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=180+-+B ALIGN=MIDDLE  ALT=\"180+-+B\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and for the 3rd triangle,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=180+-+C ALIGN=MIDDLE  ALT=\"180+-+C\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "There are exactly <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=50 ALIGN=MIDDLE  ALT=\"50\"   DISABLED_style= \"max-width:90%; height:auto;\" > of these triangles, so adding up all their angles, I get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=50%2A180 ALIGN=MIDDLE  ALT=\"50%2A180\"   DISABLED_style= \"max-width:90%; height:auto;\" > - (A + B + C + D + . . .)<BR>\n" );
document.write( "I will run out of letters, but there must be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=50 ALIGN=MIDDLE  ALT=\"50\"   DISABLED_style= \"max-width:90%; height:auto;\" > of them. Since they go<BR>\n" );
document.write( "completely around the interior point of the polygon, they add up to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=360 ALIGN=MIDDLE  ALT=\"360\"   DISABLED_style= \"max-width:90%; height:auto;\" > degress, so<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=50%2A180+-+360 ALIGN=MIDDLE  ALT=\"50%2A180+-+360\"   DISABLED_style= \"max-width:90%; height:auto;\" > degrees is the answer<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=50%2A180+-+360+=+9000+-+360 ALIGN=MIDDLE  ALT=\"50%2A180+-+360+=+9000+-+360\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9000+-+360+=+8640 ALIGN=MIDDLE  ALT=\"9000+-+360+=+8640\"   DISABLED_style= \"max-width:90%; height:auto;\" > degrees </SPAN>\n" );
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