document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=547713>Question 547713</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If an angle is 60 less than twice it's complement find the ratio of the angle to its complement.\r<BR>\n" );
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document.write( "If an angle is 30 more than twice it`s complement, find the ratio of the smaller to the larger angle. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #356512 by </B><A HREF=/tutors/aboutme.mpl?userid=mathie123><B>mathie123(224)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=mathie123><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=356512\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let's recall what complementary angles really are:<BR>\n" );
document.write( "Two angles are complement if they sum to 90 degrees.  \r<BR>\n" );
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document.write( "Okay, so for the first question we will let x be the angle so the other angle must be x-60.  Since they are each others complement we know:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-60%29%2Bx=90 ALIGN=MIDDLE  ALT=\"%28x-60%29%2Bx=90\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x-60=90 ALIGN=MIDDLE  ALT=\"2x-60=90\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x-60%2B60=90%2B60 ALIGN=MIDDLE  ALT=\"2x-60%2B60=90%2B60\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x=150 ALIGN=MIDDLE  ALT=\"2x=150\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%2F2=150%2F2 ALIGN=MIDDLE  ALT=\"2x%2F2=150%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=75 ALIGN=MIDDLE  ALT=\"x=75\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So the two angles are 75 and 75-60=15.<BR>\n" );
document.write( "This means that the ratio between the two is 75:15  which can be reduced to 5:1.  \r<BR>\n" );
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document.write( "For the second question, it is very similar...<BR>\n" );
document.write( "Let y be the angle so then the other angle is y-30.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%2B%28y-30%29=90 ALIGN=MIDDLE  ALT=\"y%2B%28y-30%29=90\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2y-30=90 ALIGN=MIDDLE  ALT=\"2y-30=90\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2y=120 ALIGN=MIDDLE  ALT=\"2y=120\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=60 ALIGN=MIDDLE  ALT=\"y=60\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So the two angles are 60 and 60-30=30.   <BR>\n" );
document.write( "This means that the ratio of the smaller to the larger angle is 30:60 which can be reduced to 1:2.   </SPAN>\n" );
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