document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=620307>Question 620307</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Angles A and B are complementary angles. If the measure of angle A is 54 degrees less than the measure of angle B, find the measures of 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 #390074 by </B><A HREF=/tutors/aboutme.mpl?userid=math-vortex><B>math-vortex(648)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math-vortex><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=math-vortex><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=390074\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Hi, there--<BR>\n" );
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document.write( "Let a be the measure of angle A in degrees.<BR>\n" );
document.write( "Let b be the measure of angle B in degrees.<BR>\n" );
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document.write( "Since the angles are complementary, their sum is 90 degrees. We can write,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2Bb=90 ALIGN=MIDDLE  ALT=\"a%2Bb=90\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "We know that \"the measure of angle A is 54 degrees less than the measure of angle B.\" In algebra, we can write,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=b-54 ALIGN=MIDDLE  ALT=\"a=b-54\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Now we have a system of equations in two variables. Solve the system to find the measure of each angle. Substitute b-54 for a in the first equation.<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2Bb=90 ALIGN=MIDDLE  ALT=\"a%2Bb=90\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28b-54%29%2Bb=90 ALIGN=MIDDLE  ALT=\"%28b-54%29%2Bb=90\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Simplify by combining like terms.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2b-54=90 ALIGN=MIDDLE  ALT=\"2b-54=90\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2b=90%2B54 ALIGN=MIDDLE  ALT=\"2b=90%2B54\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2b=144 ALIGN=MIDDLE  ALT=\"2b=144\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=72 ALIGN=MIDDLE  ALT=\"b=72\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "The measure of angle B is 72 degrees. To find the measure of angle A, substitute 72 for b in the first equation.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2Bb=90 ALIGN=MIDDLE  ALT=\"a%2Bb=90\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2B72=90 ALIGN=MIDDLE  ALT=\"a%2B72=90\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=90-72 ALIGN=MIDDLE  ALT=\"a=90-72\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=18 ALIGN=MIDDLE  ALT=\"a=18\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "The measure of angle A is 18 degrees. <BR>\n" );
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document.write( "Now we need to check our answers against the information in the problem.<BR>\n" );
document.write( "Yes, angles A and B are complementary because their angle measures add to 90 degrees (18+72=90).<BR>\n" );
document.write( "Yes, the measure of angle A is 53 degrees less than the measure of angle B (72-18=54).<BR>\n" );
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document.write( "Hope this helps! Feel free to email if you still have questions about this.<BR>\n" );
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document.write( "Ms.Figgy<BR>\n" );
document.write( "math.in.the.vortex@gmail.com<BR>\n" );
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