document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1033105>Question 1033105</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A convex polygon is a polygon whose interior angles are between 0 and 180. The number of diagonals D in a convex polygon with n sides is given by the formula D=1/2n (n-3). Determine the number of sides n in a convex polygon that has 27 diagonals by solving the equation 27=1/2n(n-3) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #647982 by </B><A HREF=/tutors/aboutme.mpl?userid=robertb><B>robertb(5830)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=robertb><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=robertb><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=647982\">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=D+=+%28n%28n-3%29%29%2F2 ALIGN=MIDDLE  ALT=\"D+=+%28n%28n-3%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > ==> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=27+=+%28n%28n-3%29%29%2F2 ALIGN=MIDDLE  ALT=\"27+=+%28n%28n-3%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > ==> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=54+=+n%5E2+-+3n ALIGN=MIDDLE  ALT=\"54+=+n%5E2+-+3n\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "==> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%5E2+-+3n+-+54+=+0 ALIGN=MIDDLE  ALT=\"n%5E2+-+3n+-+54+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >  ==> (n-9)(n+6) = 0  ==> n = 9.  (n = -6 is not acceptable.)\r<BR>\n" );
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document.write( "Therefore the convex polygon has 9 sides. </SPAN>\n" );
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