document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=746644>Question 746644</A>: <I><SPAN STYLE=\"word-break: break-all;\"> IN TRIANGLE ABC, THE MEASURE OF ANGLE B IS 32 DEGREES MORE THAN THREE TIMES THE MEASURE OF ANGLE A. THE MEASURE OF ANGLE C IS 58 DEGREE MORE THAN THE MEASURE Of ANGLE A.  THE SUM OF ALL THREE ANGLES IS 180 DEGREE.<BR>\n" );
document.write( "USE GAUSSIAN ELIMINATION AND BACKWARDS SUBSTITUTION TO FIND MEASURE OF EACH ANGLE OF THE TRIANGLE. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #454412 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39617)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=454412\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Naming the internal angles as a, b, c for the points A, B, and C,<BR>\n" );
document.write( "Three equations:   <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=32%2B3a ALIGN=MIDDLE  ALT=\"b=32%2B3a\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=58%2Ba ALIGN=MIDDLE  ALT=\"c=58%2Ba\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2Bb%2Bc=180 ALIGN=MIDDLE  ALT=\"a%2Bb%2Bc=180\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Putting into a matrix:  rearrange each equation to be in the same type of format as the \"180\" equation.<BR>\n" );
document.write( "System:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2Bb%2Bc=180 ALIGN=MIDDLE  ALT=\"a%2Bb%2Bc=180\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a-c=-58 ALIGN=MIDDLE  ALT=\"a-c=-58\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3a-b=-32 ALIGN=MIDDLE  ALT=\"3a-b=-32\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "N\r<BR>\n" );
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document.write( "Do something more to make the system.  You will need the coefficients of the variables to form the matrix.\r<BR>\n" );
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document.write( "System:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2Bb%2Bc=180 ALIGN=MIDDLE  ALT=\"a%2Bb%2Bc=180\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2B0%2Ab-c=-58 ALIGN=MIDDLE  ALT=\"a%2B0%2Ab-c=-58\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3a-b%2B0%2Ac=-32 ALIGN=MIDDLE  ALT=\"3a-b%2B0%2Ac=-32\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "This is not yet arranged for rendering on algebra.com site, but your matrix to begin will be like this:<BR>\n" );
document.write( "1___  1___  1___  180<BR>\n" );
document.write( "1___  0___  -1___  -58<BR>\n" );
document.write( "3___  -1___  0___  -32\r<BR>\n" );
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document.write( "Can you continue from that?<BR>\n" );
document.write( "This is what to try. <BR>\n" );
document.write( "Use R1 to eliminate the column 1 elements into zero in R2 and R3.  Replace R2 with R2-R1.  Replace R3 with R3-3*R1.  Can you decide what to do next? ----- </SPAN>\n" );
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