document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=233491>Question 233491</A>: <I><SPAN STYLE=\"word-break: break-all;\"> THE RATIO OF THE COMPLIMENTS OF TWO ANGLES IS 3 :5. THE RATIO OF THE SUPPLEMENTS OF THE SAME TWO ANGLES IS 6:7. WHAT ARE THE TWO ANGLES </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #172350 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=172350\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> First statement is ratio of complement of one angle to the complement of the other angle is 3/5.\r<BR>\n" );
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document.write( "If x = one angle and y = the other angle, this means that:\r<BR>\n" );
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document.write( "(90-x) / (90-y) = 3/5\r<BR>\n" );
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document.write( "Second statement is ratio of supplement of one angle to the supplement of the other angle is 6/7.\r<BR>\n" );
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document.write( "(180-x) / (180-y) = 6/7\r<BR>\n" );
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document.write( "Cross multiply and you get:\r<BR>\n" );
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document.write( "5 * (90-x) = 3 * (90-y)<BR>\n" );
document.write( "7 * (180-x) = 6 * (180-y)\r<BR>\n" );
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document.write( "Solve first equation for y and you get:\r<BR>\n" );
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document.write( "First equation is:<BR>\n" );
document.write( "5 * (90-x) = 3 * (90-y)<BR>\n" );
document.write( "Remove parentheses to get:<BR>\n" );
document.write( "5*90 - 5*x = 3*90 - 3*y<BR>\n" );
document.write( "Add 3*y to both sides and add 5*x to both sides and subtract 450 from both sides to get:<BR>\n" );
document.write( "3*y = 5*x + 270 - 450<BR>\n" );
document.write( "This becomes:<BR>\n" );
document.write( "3*y = 5*x - 180<BR>\n" );
document.write( "Divide both sides by 3 to get:<BR>\n" );
document.write( "y = (5*x-180)/3\r<BR>\n" );
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document.write( "Second equation is:<BR>\n" );
document.write( "7 * (180-x) = 6 * (180-y) becomes:<BR>\n" );
document.write( "Remove parentheses to get:<BR>\n" );
document.write( "7*180 - 7*x = 6*180 - 6*y<BR>\n" );
document.write( "add 7*x to both sides of the equation and add 6*y to both sides of the equation and subtract 7*180 from both sides of the equation to get:<BR>\n" );
document.write( "6*y = 7*x + 6*180 - 7*180<BR>\n" );
document.write( "This becomes:<BR>\n" );
document.write( "6*y = 7*x - 180\r<BR>\n" );
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document.write( "Replace y with (5*x-180)/3 in the second equation to get:\r<BR>\n" );
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document.write( "6 * (5*x-180)/3 = 7*x - 180<BR>\n" );
document.write( "This becomes:<BR>\n" );
document.write( "2 * (5*x-180) = 7*x - 180<BR>\n" );
document.write( "This becomes:<BR>\n" );
document.write( "10*x - 360 = 7*x - 180<BR>\n" );
document.write( "Subtract 7*x from both sides and add 360 to both sides to get:<BR>\n" );
document.write( "3*x = 180<BR>\n" );
document.write( "Divide both sides by 3 to get:<BR>\n" );
document.write( "x = 60\r<BR>\n" );
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document.write( "You now have x = 60 degrees.\r<BR>\n" );
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document.write( "Go back to the first ratio to get:\r<BR>\n" );
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document.write( "First ratio is:<BR>\n" );
document.write( "(90-x)/(90-y) = 3/5<BR>\n" );
document.write( "Replace x with 60 to get:<BR>\n" );
document.write( "(90-60)/(90-y) = 3/5<BR>\n" );
document.write( "This becomes:<BR>\n" );
document.write( "30/(90-y) = 3/5<BR>\n" );
document.write( "multiply both sides by 5 and multiply both sides by (90-y) to get:<BR>\n" );
document.write( "30*5 = 3 * (90-y)<BR>\n" );
document.write( "Simplify and remove parentheses to getr:<BR>\n" );
document.write( "150 = 270 - 3*y<BR>\n" );
document.write( "Add 3*y to both sides and subtract 150 from both sides to get:<BR>\n" );
document.write( "3*y = 270-150 = 120<BR>\n" );
document.write( "Divide both sides by 3 to get:<BR>\n" );
document.write( "y = 40\r<BR>\n" );
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document.write( "You have:<BR>\n" );
document.write( "x = 60<BR>\n" );
document.write( "y = 40\r<BR>\n" );
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document.write( "Plug these values into your original equation to prove these answers are good.\r<BR>\n" );
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document.write( "(90-x)/(90-y) = 3/5 becomes (90-60)/(90-40) = 3/5 becomes 30/50 = 3/5 becomes 3/5 = 3/5 which is true.\r<BR>\n" );
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document.write( "(180-x)/180-y) = 6/7 becomes (180-60) / (180-40) = 3/5 becomes 120 / 140 = 6/7 becomes 12/14 = 6/7 becomes 6/7 = 6/7 which is true.\r<BR>\n" );
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document.write( "Both answer are confirmed to be good.\r<BR>\n" );
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document.write( "Your answer is:\r<BR>\n" );
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document.write( "The two angles are 40 degrees and 60 degrees.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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