document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1105956>Question 1105956</A>: <I><SPAN STYLE=\"word-break: break-all;\"> two angles are supplementary. If one angle is doubled, the result is 69% less than the other angle. Find the angles </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #720875 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=720875\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> let x = the first angle<BR>\n" );
document.write( "let y = the second angle.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "if the angles are supplementary, their sum is 180 degrees.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "x + y = 180\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "if one angle is doubled, the result is 69% less than the other angle.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "let x be the angle that's doubled.<BR>\n" );
document.write( "let y be the angle that is 69% less.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "2x = y - .69y\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "simplify this to get 2x = .31y.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "you have 2 equations that need to be solved simultaneously.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "they are:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "x + y = 180<BR>\n" );
document.write( "2x = .31y\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "rearrange the second equation to get 2x - .31y = 0\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "your two equations are now:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "x + y = 180<BR>\n" );
document.write( "2x - .31y = 0\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "multiply both sides of the first equation by 2 and leave the second equation as is to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "2x + 2y = 360<BR>\n" );
document.write( "2x - .31y = 0\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "subtract the second equation from the first to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "2.31y = 360\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "solve for y to get y = 360 / 2.31 = 155.8441558 degrees.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "since x + y = 180, then x = 180 - y = 24.15584416 degrees.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "2x = 48.31168831 degrees.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "y - .69y = 48.31168831 degrees.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "looks like the problem is solved.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the angles are 155.8441558 and 24.15584416 degrees.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );