document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=106211>Question 106211</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0866099654/algebrahomeworkh>Geometry</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> Can some one please help me solve this problem?<BR>\n" );
document.write( "The ratio of the complements of two angles is 3:2 and the ratio of their<BR>\n" );
document.write( "supplements is 9:8. Find the two original angles.\r<BR>\n" );
document.write( "\n" );
document.write( "Thank you! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #77256 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=77256\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The ratio of the complements of two angles is 3:2 and the ratio of their<BR>\n" );
document.write( "supplements is 9:8. Find the two original angles.<BR>\n" );
document.write( "----------------<BR>\n" );
document.write( "Let the two angles be x and y.<BR>\n" );
document.write( "The complements are 90-x and 90-y<BR>\n" );
document.write( "The supplements are 180-x and 180-y<BR>\n" );
document.write( "------------------------<BR>\n" );
document.write( "EQUATIONS:<BR>\n" );
document.write( "1st: (90-x)/(90-y) = 3/2<BR>\n" );
document.write( "2nd: (180-x)/(180-y) = 9/8<BR>\n" );
document.write( "---------------------------<BR>\n" );
document.write( "Simplifying 1st you get:<BR>\n" );
document.write( "2(90-x) = 3(90-y)<BR>\n" );
document.write( "180-2x = 270-3y<BR>\n" );
document.write( "2x-3y = -90<BR>\n" );
document.write( "---------------<BR>\n" );
document.write( "Simplifying 2nd you get:<BR>\n" );
document.write( "8(180-x)= 9(180-y)<BR>\n" );
document.write( "8*180-8x = 9*180-9y<BR>\n" );
document.write( "8x-9y = -180<BR>\n" );
document.write( "----------------<BR>\n" );
document.write( "Rewrite 1st and 2nd:<BR>\n" );
document.write( "1st: 2x-3y = -90<BR>\n" );
document.write( "2nd: 8x-9y = -180<BR>\n" );
document.write( "--------------------<BR>\n" );
document.write( "Multiply 1st by 4 and solve for y:<BR>\n" );
document.write( "1st: 8x - 12y = -360<BR>\n" );
document.write( "Subtract from 2nd to get:<BR>\n" );
document.write( "3y = 180<BR>\n" );
document.write( "y = 60<BR>\n" );
document.write( "----------<BR>\n" );
document.write( "Substitute into 2x-3y = -90 to solve for x:<BR>\n" );
document.write( "2x-3*60= -90<BR>\n" );
document.write( "2x = 90<BR>\n" );
document.write( "x = 45 <BR>\n" );
document.write( "=============<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.  </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );