document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=562200>Question 562200</A>: <I><SPAN STYLE=\"word-break: break-all;\"> There is a famous theorem in Euclidean geometry that states that the sum of<BR>\n" );
document.write( "the interior angles of a triangle is 180.<BR>\n" );
document.write( "(a) Use the theorem about triangles to determine the sum of the angles of<BR>\n" );
document.write( "a convex quadrilateral.<BR>\n" );
document.write( "(b) Use the result in Part (1) to determine the sum of the angles of a convex<BR>\n" );
document.write( "pentagon.<BR>\n" );
document.write( "(c) Use the result in Part (2) to determine the sum of the angles of a convex<BR>\n" );
document.write( "hexagon.<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 #364476 by </B><A HREF=/tutors/aboutme.mpl?userid=richard1234><B>richard1234(7193)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=richard1234><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=richard1234><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=364476\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> a) Quadrilateral can be divided into two triangles (each with vertices at the vertices of the quadrilateral) so the sum of the angles is 2*180 = 360\r<BR>\n" );
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document.write( "b) Same logic as a) but now we can divide into three triangles --> 3*180 = 540\r<BR>\n" );
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document.write( "c) 4*180 = 720\r<BR>\n" );
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document.write( "We can generalize to n sides and derive the sum of the angles of an n-gon to be 180(n-2). </SPAN>\n" );
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