document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=733053>Question 733053</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In the diagram of triangle ABC, side BC is extended to D\r<BR>\n" );
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document.write( "If m<A= x^2-6x , m<B= 2x-3, and m<ACD= 9x+27, what is the value of x? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #448247 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=448247\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If \r<BR>\n" );
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document.write( "m< <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=+x%5E2-6x ALIGN=MIDDLE  ALT=\"A=+x%5E2-6x\"   DISABLED_style= \"max-width:90%; height:auto;\" > , <BR>\n" );
document.write( "m< <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B=+2x-3 ALIGN=MIDDLE  ALT=\"B=+2x-3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <BR>\n" );
document.write( "m< <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ACD=+9x%2B27 ALIGN=MIDDLE  ALT=\"ACD=+9x%2B27\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <BR>\n" );
document.write( "what is the value of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" >?\r<BR>\n" );
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document.write( "recall:\r<BR>\n" );
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document.write( "The exterior angle theorem: the exterior angle of a triangle is equal to the sum of the two remote interior angles\r<BR>\n" );
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document.write( "so, m< <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ACD ALIGN=MIDDLE  ALT=\"ACD\"   DISABLED_style= \"max-width:90%; height:auto;\" >=m< <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A ALIGN=MIDDLE  ALT=\"A\"   DISABLED_style= \"max-width:90%; height:auto;\" >+ m< <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B ALIGN=MIDDLE  ALT=\"B\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "then you have\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9x%2B27=x%5E2-6x%2B2x-3 ALIGN=MIDDLE  ALT=\"9x%2B27=x%5E2-6x%2B2x-3\"   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=9x%2B27=x%5E2-4x-3 ALIGN=MIDDLE  ALT=\"9x%2B27=x%5E2-4x-3\"   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=x%5E2-4x-9x-3-27=0 ALIGN=MIDDLE  ALT=\"x%5E2-4x-9x-3-27=0\"   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=x%5E2-13x-30=0 ALIGN=MIDDLE  ALT=\"x%5E2-13x-30=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >...factor...replace <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-13x ALIGN=MIDDLE  ALT=\"-13x\"   DISABLED_style= \"max-width:90%; height:auto;\" > with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-15x%2B2x ALIGN=MIDDLE  ALT=\"-15x%2B2x\"   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=x%5E2-15x%2B2x-30=0 ALIGN=MIDDLE  ALT=\"x%5E2-15x%2B2x-30=0\"   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=%28x%5E2-15x%29%2B%282x-30%29=0 ALIGN=MIDDLE  ALT=\"%28x%5E2-15x%29%2B%282x-30%29=0\"   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=x%28x-15%29%2B2%28x-15%29=0 ALIGN=MIDDLE  ALT=\"x%28x-15%29%2B2%28x-15%29=0\"   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=%28x%2B2%29%28x-15%29=0 ALIGN=MIDDLE  ALT=\"%28x%2B2%29%28x-15%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "so, if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B2=0 ALIGN=MIDDLE  ALT=\"x%2B2=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >...=>...<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-2 ALIGN=MIDDLE  ALT=\"x=-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >....this solution make equation true, but it could not work with angle measure because it cannot be negative\r<BR>\n" );
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document.write( " if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-15=0 ALIGN=MIDDLE  ALT=\"x-15=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >...=>...<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=15 ALIGN=MIDDLE  ALT=\"x=15\"   DISABLED_style= \"max-width:90%; height:auto;\" >...so, your solution is:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x+=+15%29+ ALIGN=MIDDLE  ALT=\"highlight%28x+=+15%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "now find the measure of each angle:\r<BR>\n" );
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document.write( "m< <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=+15%5E2-6%2A15 ALIGN=MIDDLE  ALT=\"A=+15%5E2-6%2A15\"   DISABLED_style= \"max-width:90%; height:auto;\" >...=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=+225-90 ALIGN=MIDDLE  ALT=\"A=+225-90\"   DISABLED_style= \"max-width:90%; height:auto;\" >..=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=+135 ALIGN=MIDDLE  ALT=\"A=+135\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "m< <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B=+2%2A15-3 ALIGN=MIDDLE  ALT=\"B=+2%2A15-3\"   DISABLED_style= \"max-width:90%; height:auto;\" >...=> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B=30-3 ALIGN=MIDDLE  ALT=\"B=30-3\"   DISABLED_style= \"max-width:90%; height:auto;\" >..=> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B=27 ALIGN=MIDDLE  ALT=\"B=27\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "m< <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ACD=+9%2A15%2B27 ALIGN=MIDDLE  ALT=\"ACD=+9%2A15%2B27\"   DISABLED_style= \"max-width:90%; height:auto;\" >...=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ACD=+135%2B27 ALIGN=MIDDLE  ALT=\"ACD=+135%2B27\"   DISABLED_style= \"max-width:90%; height:auto;\" >..=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ACD=+162 ALIGN=MIDDLE  ALT=\"ACD=+162\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );