document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=462566>Question 462566</A>: <I><SPAN STYLE=\"word-break: break-all;\"> &#8736;PQR and &#8736;ABC are complementary angles and &#8736;PQR is four times as large as &#8736;ABC. Determine the measure of each angle. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #317081 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=317081\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> &#8736;PQR and &#8736;ABC are complementary angles and &#8736;PQR is four times as large as &#8736;ABC. Determine the measure of each angle.<BR>\n" );
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document.write( "A big part of solving this problem is knowing how to translate an English sentence in to algebraic language.<BR>\n" );
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document.write( "Let<BR>\n" );
document.write( "x = the measure of &#8736;PQR <BR>\n" );
document.write( "y = the measure of &#8736;ABC<BR>\n" );
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document.write( "We know that the two angles are complementary. By definition, the sum of their measures is 90 degrees. We can write this as an equation:<BR>\n" );
document.write( "[the measure of &#8736;PQR] + [the measure of &#8736;ABC] = 90 degrees<BR>\n" );
document.write( "x + y = 90<BR>\n" );
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document.write( "We also know that &#8736;PQR is four times as large as &#8736;ABC. Let's translate this into algebraic equation.<BR>\n" );
document.write( "[the measure of &#8736;PQR] = 4 *  [the measure of &#8736;ABC]<BR>\n" );
document.write( "y = 4 * x<BR>\n" );
document.write( "y = 4x<BR>\n" );
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document.write( "Now we have two equations in two variables. Let's solve for x and y.<BR>\n" );
document.write( "x + y = 90<BR>\n" );
document.write( "y = 4x<BR>\n" );
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document.write( "Substitute 4x for y in the first equation, and solve for x.<BR>\n" );
document.write( "x + y = 90<BR>\n" );
document.write( "x + (4x) = 90<BR>\n" );
document.write( "5x = 90<BR>\n" );
document.write( "x = 18<BR>\n" );
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document.write( "Substitute 18 for x in the second equation, and solve for y.<BR>\n" );
document.write( "y = 4x<BR>\n" );
document.write( "y = 4(18)<BR>\n" );
document.write( "y = 72<BR>\n" );
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document.write( " <BR>\n" );
document.write( "We see that the measure of &#8736;PQR is 18 degrees and and the measure of &#8736;ABC is 72 degrees.\r<BR>\n" );
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document.write( "18 + 72 = 90, so the two angles are complementary.<BR>\n" );
document.write( "72 = 4(18), so &#8736;PQR is four times as large as &#8736;ABC.<BR>\n" );
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document.write( "hope this helps!<BR>\n" );
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document.write( "Ms.Figgy<BR>\n" );
document.write( "math.in.the.vortex </SPAN>\n" );
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