document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=890297>Question 890297</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The difference if the measures of angle A and angle B is 80, where the measure of angle A is greater than that of angle B. The sum of the measures of the supplement of the complement of angle B and the supplement of angle A is forty more than three times the measure of the complement of angle B. What are the measures of angle A and angle B? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #538877 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=538877\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the equations are shown below.\r<BR>\n" );
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document.write( "A > B\r<BR>\n" );
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document.write( "A - B = 80\r<BR>\n" );
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document.write( "complement of B is equal to (90 - B)\r<BR>\n" );
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document.write( "supplement of complement of B is equal to (180 - (90 - B))\r<BR>\n" );
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document.write( "supplement of A is equal to (180 - A)\r<BR>\n" );
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document.write( "the sum of the measures of the supplement of the complement of angle B and the supplement of angle A is forty more than three times the measure of the complement of angle B becomes:\r<BR>\n" );
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document.write( "(180 - (90 - B) + (180 - A) = 3 * (90 - B) + 40\r<BR>\n" );
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document.write( "simplify this formula to get:\r<BR>\n" );
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document.write( "180 - 90 + B + 180 - A = 270 - 3B + 40\r<BR>\n" );
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document.write( "simplify this to get:\r<BR>\n" );
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document.write( "270 + B - A = 310 - 3B\r<BR>\n" );
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document.write( "subtract 270 and subtract B from both sides of this equation to get;\r<BR>\n" );
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document.write( "-A = 40 - 4B\r<BR>\n" );
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document.write( "multiply both sides of this equation by -1 to get:\r<BR>\n" );
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document.write( "A = 4B - 40\r<BR>\n" );
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document.write( "you know that A - B = 80 which means that A = B + 80\r<BR>\n" );
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document.write( "Replace A in the equation of A = 4B - 40 to get:\r<BR>\n" );
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document.write( "B + 80 = 4B - 40\r<BR>\n" );
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document.write( "add 40 to both sides of this equation and subtract B from both sides of this equation to get:\r<BR>\n" );
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document.write( "120 = 3B\r<BR>\n" );
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document.write( "solve for B to get:\r<BR>\n" );
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document.write( "B = 40\r<BR>\n" );
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document.write( "since A = B + 80, then A = 120.\r<BR>\n" );
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document.write( "that should be your answer.\r<BR>\n" );
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document.write( "confirm by going back to the original equations to see if all the statments made there hold true.\r<BR>\n" );
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document.write( "A - B = 80 becomes 120 - 40 = 80 which becomes 80 = 80 so that statement is true.\r<BR>\n" );
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document.write( "A > B becomes 120 > 40 so that statement is true.\r<BR>\n" );
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document.write( "The sum of the measures of the supplement of the complement of angle B and the supplement of angle A is forty more than three times the measure of the complement of angle B leads to the formula shown below:\r<BR>\n" );
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document.write( "(180 - (90 - B) + (180 - A) = 3 * (90 - B) + 40\r<BR>\n" );
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document.write( "replace A with 120 and B with 40 in this equation to get:\r<BR>\n" );
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document.write( "(180 - (90 - 40) + (180 - 120) = 3 * (90 - 40) + 40\r<BR>\n" );
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document.write( "simplify this equation to get:\r<BR>\n" );
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document.write( "130 + 60 = 3 * (50) + 40\r<BR>\n" );
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document.write( "simplify further to get:\r<BR>\n" );
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document.write( "190 = 150 + 40\r<BR>\n" );
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document.write( "simplify further to get:\r<BR>\n" );
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document.write( "190 = 190 which is true, so the statement leading to this formula is true when A = 120 and B = 40.\r<BR>\n" );
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document.write( "looks like the solution is good.\r<BR>\n" );
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document.write( "A = 120<BR>\n" );
document.write( "B = 40\r<BR>\n" );
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document.write( " </SPAN>\n" );
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