document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=182998>Question 182998</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 9. In a certain triangle the measure of one angle is double the measure of a second angle but is 10 degrees less than the measure of the third angle. [The sum of the measures of three interior angles of a triangle is always 180 degrees.]  What is 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 #137456 by </B><A HREF=/tutors/aboutme.mpl?userid=MathGuyJoe><B>MathGuyJoe(20)</B></A><img src=\"/images/stars/stars-06.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathGuyJoe><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=137456\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let a, b and c be the 3 angles.  Since there are 3 variables, we're gonna need (at least) 3 equations to solve for them.  Being a triangle we know:\r<BR>\n" );
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document.write( "Equation 1:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+a+%2B+b+%2B+c+=+360+ ALIGN=MIDDLE  ALT=\"+a+%2B+b+%2B+c+=+360+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "\"one angle is double the measure of a second angle\":\r<BR>\n" );
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document.write( "Equation 2:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+a+=+2b+ ALIGN=MIDDLE  ALT=\"+a+=+2b+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "\"but is 10 degrees less than the measure of the third angle\":\r<BR>\n" );
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document.write( "Equation 3:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+a+=+c+-+10+ ALIGN=MIDDLE  ALT=\"+a+=+c+-+10+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Let's re-write equations 2 & 3 in terms of \"a\" so we can substitute them into equation 1.<BR>\n" );
document.write( "Equation 2 can be rewritten as:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+b+=+a%2F2+ ALIGN=MIDDLE  ALT=\"+b+=+a%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Equation 3 can be rewritten as:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+c+=+a+%2B+10+ ALIGN=MIDDLE  ALT=\"+c+=+a+%2B+10+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Substituting back into Equation 1 gives us:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+a+%2B+%28a%2F2%29+%2B+%28a+%2B+10%29+=+360+ ALIGN=MIDDLE  ALT=\"+a+%2B+%28a%2F2%29+%2B+%28a+%2B+10%29+=+360+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "I prefer not to work with fractions if I can help it, so let's multiply every element, on both sides, by 2:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2a+%2B+a+%2B+2a+%2B+20+=+720+ ALIGN=MIDDLE  ALT=\"+2a+%2B+a+%2B+2a+%2B+20+=+720+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Group the a's:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+5a+%2B+20+=+720+ ALIGN=MIDDLE  ALT=\"+5a+%2B+20+=+720+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Subtract 20 from both sides:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+5a+=+700+ ALIGN=MIDDLE  ALT=\"+5a+=+700+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Divide both sides by 5:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+a+=+140+ ALIGN=MIDDLE  ALT=\"+a+=+140+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Now we can substitute a back into our \"modified\" Equations 2 & 3 to solve for b & c:<BR>\n" );
document.write( "Equation 2:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+b+=+a%2F2+ ALIGN=MIDDLE  ALT=\"+b+=+a%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+b+=+%28140%29+%2F+2+ ALIGN=MIDDLE  ALT=\"+b+=+%28140%29+%2F+2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+b+=+70+ ALIGN=MIDDLE  ALT=\"+b+=+70+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Equation 3:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+c+=+a+%2B+10+ ALIGN=MIDDLE  ALT=\"+c+=+a+%2B+10+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+c+=+%28140%29+%2B+10+ ALIGN=MIDDLE  ALT=\"+c+=+%28140%29+%2B+10+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+c+=+150+ ALIGN=MIDDLE  ALT=\"+c+=+150+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "So our angles are <b>140</b>, <b>70</b> and <b>150</b>.<BR>\n" );
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document.write( "Hope this helps. ~ Joe </SPAN>\n" );
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