document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1062720>Question 1062720</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The sum of the measure of the interior angles of a polygon is 1800 degrees. Determine the number of sides for the polygon.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #677705 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=677705\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%2812%29 ALIGN=MIDDLE  ALT=\"highlight%2812%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Relying on formulas, you would have memorized that,<BR>\n" );
document.write( "for a polygon with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n ALIGN=MIDDLE  ALT=\"n\"   DISABLED_style= \"max-width:90%; height:auto;\" > sides, that sum is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28n-2%29%2A180%5Eo ALIGN=MIDDLE  ALT=\"%28n-2%29%2A180%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "and in this case<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n-2=1800%5Eo%2F180%5Eo=10 ALIGN=MIDDLE  ALT=\"n-2=1800%5Eo%2F180%5Eo=10\"   DISABLED_style= \"max-width:90%; height:auto;\" >----><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n=10%2B2=12 ALIGN=MIDDLE  ALT=\"n=10%2B2=12\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( " <BR>\n" );
document.write( "Relying on ideas, you would remember how, in a convex polygon,<BR>\n" );
document.write( "all the diagonals drawn from one vertex divide it into triangles<BR>\n" );
document.write( "(two less triangles than the number of sides);<BR>\n" );
document.write( "the angles of those triangles are the interior angles of the polygon,<BR>\n" );
document.write( "and that, with a sum of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=180%5Eo ALIGN=MIDDLE  ALT=\"180%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" > per triangle, you would have<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1800%5Eo%2F180%5Eo=10 ALIGN=MIDDLE  ALT=\"1800%5Eo%2F180%5Eo=10\"   DISABLED_style= \"max-width:90%; height:auto;\" > triangles.<BR>\n" );
document.write( " <BR>\n" );
document.write( "Or maybe you would think of those incredibly useful exterior angles.<BR>\n" );
document.write( "The exterior angles measure how much your direction changes at each vertex as you go around the polygon.<BR>\n" );
document.write( "Of course, each exterior angle is attached to an exterior angle,<BR>\n" );
document.write( "and they are supplementary, meaning that the pair of angles adds to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=180%5Eo ALIGN=MIDDLE  ALT=\"180%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "All the exterior angles add up to a whole turn around the polygon;<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=360%5Eo=2%2A180%5Eo ALIGN=MIDDLE  ALT=\"360%5Eo=2%2A180%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "For the polygon in this question, the sum of all exterior and interior angles is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1800%5Eo%2B2%2A180%5Eo=10%2A180%5Eo%2B2%2A180%5Eo=12%2A180%5Eo ALIGN=MIDDLE  ALT=\"1800%5Eo%2B2%2A180%5Eo=10%2A180%5Eo%2B2%2A180%5Eo=12%2A180%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "That means <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12 ALIGN=MIDDLE  ALT=\"12\"   DISABLED_style= \"max-width:90%; height:auto;\" > interior-exterior pairs,<BR>\n" );
document.write( "meaning <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12 ALIGN=MIDDLE  ALT=\"12\"   DISABLED_style= \"max-width:90%; height:auto;\" > angles in that polygon. </SPAN>\n" );
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