document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=949307>Question 949307</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The sum of all but one of the angles of a particular convex polygon is 1578 degrees. What is the measure, in degrees, of the remaining interior angle? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #579592 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=579592\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The measure of each (interior) angle in a convex polygon is less than <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( "The sum of the measures of all the (interior) angles of a convex 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 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( "Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8%2A180%5Eo=1440%5Eo%3C1578%5Eo ALIGN=MIDDLE  ALT=\"8%2A180%5Eo=1440%5Eo%3C1578%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9%2A180%5Eo=1620%5Eo%3E1578%5Eo ALIGN=MIDDLE  ALT=\"9%2A180%5Eo=1620%5Eo%3E1578%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "we know that the polygon must have at least<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n-2=9 ALIGN=MIDDLE  ALT=\"n-2=9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n=9%2B2=11 ALIGN=MIDDLE  ALT=\"n=9%2B2=11\"   DISABLED_style= \"max-width:90%; height:auto;\" > sides.<BR>\n" );
document.write( " <BR>\n" );
document.write( "Could it have <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%3E=12 ALIGN=MIDDLE  ALT=\"n%3E=12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n-2%3E=10 ALIGN=MIDDLE  ALT=\"n-2%3E=10\"   DISABLED_style= \"max-width:90%; height:auto;\" > ?<BR>\n" );
document.write( "That would make the sum of the measures of all its angles at least<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%2A180%5E8=1800%5Eo ALIGN=MIDDLE  ALT=\"10%2A180%5E8=1800%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" > , and then, the measure of the remaining interior angle would be at least<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1800%5Eo-1578%5Eo=222%5Eo%3E180%5Eo ALIGN=MIDDLE  ALT=\"1800%5Eo-1578%5Eo=222%5Eo%3E180%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( " <BR>\n" );
document.write( "Then, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n-2=9 ALIGN=MIDDLE  ALT=\"n-2=9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n=9%2B2=11 ALIGN=MIDDLE  ALT=\"n=9%2B2=11\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "and the sum of the measures of all the (interior) angles is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9%2A180%5Eo=1620%5Eo%3E1578%5Eo ALIGN=MIDDLE  ALT=\"9%2A180%5Eo=1620%5Eo%3E1578%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "The measure of the remaining interior angle is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1620%5Eo-1578%5Eo=highlight%2842%5Eo%29 ALIGN=MIDDLE  ALT=\"1620%5Eo-1578%5Eo=highlight%2842%5Eo%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > . </SPAN>\n" );
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