document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=10910>Question 10910</A>: <I><SPAN STYLE=\"word-break: break-all;\"> One angle of a triangle is 2 degrees larger than another angle.  The sum of these two angles is 28 degrees larger than the third angle.  How large are the three angles? \r<BR>\n" );
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document.write( "x+2+x=y+28?<BR>\n" );
document.write( "2x+2=y+28?<BR>\n" );
document.write( "then what??? (assuming this is the right set up) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #5759 by </B><A HREF=/tutors/aboutme.mpl?userid=kinupanda><B>kinupanda(9)</B></A><img src=\"/images/stars/stars-05.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=kinupanda><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=5759\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> We have three angles: one angle is two degrees larger than another.  Let's define the smaller of these two angles as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  Thus, we can define the larger angle in terms of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" >, as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B2 ALIGN=MIDDLE  ALT=\"x%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "We can also define the third angle in terms of the other two!  The problem tells us that the sum of the first two angles, e.g., <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2Bx%2B2 ALIGN=MIDDLE  ALT=\"x%2Bx%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, is 28 degrees larger than the third.  Rewording this, we know that the third angle is 28 degrees *smaller* than the sum of the other two.  Thus, the measure of the third angle is equal to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2Bx%2B2%29+-+28 ALIGN=MIDDLE  ALT=\"%28x%2Bx%2B2%29+-+28\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Ax+-+26 ALIGN=MIDDLE  ALT=\"2%2Ax+-+26\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "So now we have three expressions for the angles of this triangle: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B2 ALIGN=MIDDLE  ALT=\"x%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Ax-26 ALIGN=MIDDLE  ALT=\"2%2Ax-26\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  But how do we solve 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;\" >?\r<BR>\n" );
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document.write( "Remember, in any triangle, the sum of the measures of the angles is always 180 degrees.  Thus: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%29+%2B+%28x%2B2%29+%2B+%282%2Ax-26%29+=+180 ALIGN=MIDDLE  ALT=\"%28x%29+%2B+%28x%2B2%29+%2B+%282%2Ax-26%29+=+180\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Simplifying this yields:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2Bx%2Bx%29%2B%282-26%29+=+180 ALIGN=MIDDLE  ALT=\"%28x%2Bx%2Bx%29%2B%282-26%29+=+180\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x+-+24+=+180 ALIGN=MIDDLE  ALT=\"4x+-+24+=+180\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x+=+204 ALIGN=MIDDLE  ALT=\"4x+=+204\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+51 ALIGN=MIDDLE  ALT=\"x+=+51\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now, we substitute x into the expressions we calculated earlier.  Thus, the measure of the first angle is equal to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+51 ALIGN=MIDDLE  ALT=\"x+=+51\"   DISABLED_style= \"max-width:90%; height:auto;\" > degrees, the second is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B2%29+=+%2851%2B2%29+=+53 ALIGN=MIDDLE  ALT=\"%28x%2B2%29+=+%2851%2B2%29+=+53\"   DISABLED_style= \"max-width:90%; height:auto;\" > degrees, and the third is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Ax-26+=+2%2A%2851%29-26+=+76 ALIGN=MIDDLE  ALT=\"2%2Ax-26+=+2%2A%2851%29-26+=+76\"   DISABLED_style= \"max-width:90%; height:auto;\" > degrees.\r<BR>\n" );
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document.write( "Thus, our triangle's angles are 51, 53, and 76 degrees.  To verify that this solution is correct, we just need to add them up.  Sure enough, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=51%2B53%2B76+=+180 ALIGN=MIDDLE  ALT=\"51%2B53%2B76+=+180\"   DISABLED_style= \"max-width:90%; height:auto;\" >, which we know should be the sum of the angles of a triangle. </SPAN>\n" );
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