document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=309139>Question 309139</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In quadrilateral ABCD, angle A + angle C is 2 times angle B + angle D.  If angle A = 40, then angle B =<BR>\n" );
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document.write( "(A)  60<BR>\n" );
document.write( "(B)  80<BR>\n" );
document.write( "(C)  120<BR>\n" );
document.write( "(D)  240<BR>\n" );
document.write( "(E)  It cannot be determined from the information given. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #221020 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=221020\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Garamond\" size=\"+2\">\r<BR>\n" );
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document.write( "You don't have enough information to determine the measure of angle B.  Here's why:\r<BR>\n" );
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document.write( "Since this is a quadrilateral, the sum of the interior angles is:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ (4\ -\ 2)180^\circ\ =\ 360^\circ\">\r<BR>\n" );
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document.write( "Hence:\r<BR>\n" );
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document.write( "Eq. 1:  <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ A\ +\ B\ +\ C\ +\ D\ =\ 360^\circ\">\r<BR>\n" );
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document.write( "We also know that\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ A\ =\ 40^\circ\">\r<BR>\n" );
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document.write( "And that \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ A\ +\ C\ =\ 2(B\ +\ D)\">\r<BR>\n" );
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document.write( "which is to say\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ B\ +\ D\ =\ \frac{A}{2}\ +\ \frac{C}{2}\">\r<BR>\n" );
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document.write( "Substituting for <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large B\ +\ D\"> in Eq. 1:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ A\ +\ \frac{A}{2}\ +\ C\ +\ \frac{C}{2}\ =\ 360^\circ\">\r<BR>\n" );
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document.write( "And we then know that\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ A\ +\ C\ =\ 240^\circ\">\r<BR>\n" );
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document.write( "from which we can determine that\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ C\ =\ 200^\circ\">\r<BR>\n" );
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document.write( "But the only thing we know beyond that is that:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ B\ +\ D\ =\ 120^\circ\">\r<BR>\n" );
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document.write( "And from that we can deduce that:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 0^\circ\ <\ B\ <\ 120^\circ\">\r<BR>\n" );
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document.write( "But whether that is <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE 60^\circ\"> or <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE 80^\circ\"> or any other positive number less than <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE 120^\circ\"> we have no idea.\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi} + 1 = 0\"><BR>\n" );
document.write( "</font> </SPAN>\n" );
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