document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=316144>Question 316144</A>: <I><SPAN STYLE=\"word-break: break-all;\"> one of 2 complementary angles measures 15 degree increased by half of the other. find the measure of both angles.<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #226228 by </B><A HREF=/tutors/aboutme.mpl?userid=moshiz08><B>moshiz08(60)</B></A><img src=\"/images/stars/stars-08.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=moshiz08><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=moshiz08><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=226228\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Lets call the two angles <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" >. One of them is 15 + half of the other one. Written as an equation, this says <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+15+%2B+y%2F2+ ALIGN=MIDDLE  ALT=\"x+=+15+%2B+y%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" > (eq1). \r<BR>\n" );
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document.write( "Since they are complimentary, we know that the angles add up to 90 degrees. Thus <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+%2B+y+=+90 ALIGN=MIDDLE  ALT=\"x+%2B+y+=+90\"   DISABLED_style= \"max-width:90%; height:auto;\" >. We can rewrite this as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+90+-+y ALIGN=MIDDLE  ALT=\"x+=+90+-+y\"   DISABLED_style= \"max-width:90%; height:auto;\" > (eq2). \r<BR>\n" );
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document.write( "Now (eq2) gives us an equation for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > that we can substitute into (eq1). \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+90+-++y+=+15+%2B+y%2F2 ALIGN=MIDDLE  ALT=\"x+=+90+-++y+=+15+%2B+y%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >. \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+90+-+y+=+15+%2B+y%2F2+ ALIGN=MIDDLE  ALT=\"+90+-+y+=+15+%2B+y%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "Add y to both sides to get \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+90+=+15+%2B+3y%2F2+ ALIGN=MIDDLE  ALT=\"+90+=+15+%2B+3y%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "Subtract 15 from both sides to get \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+75+=+3y%2F2+ ALIGN=MIDDLE  ALT=\"+75+=+3y%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "Multiply both sides by 2 to get \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+150+=+3+y ALIGN=MIDDLE  ALT=\"+150+=+3+y\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "Divide both sides by 3 to get \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+50++=+y+ ALIGN=MIDDLE  ALT=\"+50++=+y+\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "Thus, from (eq2), we know that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=90-y=90-50=40 ALIGN=MIDDLE  ALT=\"x=90-y=90-50=40\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "Now we check: 40 and 50 do add up to 90, so they are complimentary. \r<BR>\n" );
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document.write( "Also, one of them is 15 plus half of the other since \r<BR>\n" );
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document.write( "15 + half of 50 = 15 + 25 = 40  </SPAN>\n" );
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