document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=221519>Question 221519</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The second angle of a triangle is 4 times as large as the first. The third angle is 120° more<BR>\n" );
document.write( "than the sum of the other two angles. Find the measure of the second angle. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #166134 by </B><A HREF=/tutors/aboutme.mpl?userid=drj><B>drj(1380)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=drj><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=drj><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=166134\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The second angle of a triangle is 4 times as large as the first. The third angle is 120° more than the sum of the other two angles. Find the measure of the second angle.\r<BR>\n" );
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document.write( "Step 1.  Three angles of a triangle add up to 180 degrees.\r<BR>\n" );
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document.write( "Step 2.  Let x be the first angle.\r<BR>\n" );
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document.write( "Step 3.  Let 4x be the second angle since it's 4 times as large as the first.\r<BR>\n" );
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document.write( "Step 4.  Let x+4x=5x be the sum of the first and second angles.\r<BR>\n" );
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document.write( "Step 5.  Let 5x+120 be the third angle since it's 120 degrees more than the sum of the other two angles.\r<BR>\n" );
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document.write( "Step 6.  Then, x+4x+5x+120=180 since the three angles add up to 180\r<BR>\n" );
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document.write( "Step 7.  Solving the equation in Step 6 yields the following steps\r<BR>\n" );
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document.write( " <TR><TD  ALIGN=MIDDLE>Solved by <A  rel=nofollow HREF=http://wiki.algebra.com/index.php/Tutoring_-_pluggable_solvers>pluggable</A> solver: <A  rel=nofollow HREF=explain_simplification.solver>EXPLAIN simplification of an expression</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT><B>Your Result</B>: <BR><BR>\n" );
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document.write( "  YOUR ANSWER\n" );
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document.write( "<LI><B>This is an <A  rel=nofollow HREF=/algebra/homework/equations/>equation</A>!</B> Solutions: <FONT SIZE=+2><U><B>x=6</B></U></FONT>.<BR></LI>\n" );
document.write( "<LI><B>Graphical form</B>: <A  rel=nofollow HREF=/algebra/homework/equations/>Equation</A> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B4x%2B5x%2B120=180 ALIGN=MIDDLE  ALT=\"x%2B4x%2B5x%2B120=180\"   DISABLED_style= \"max-width:90%; height:auto;\" > was fully solved.</LI><LI><B>Text form</B>: x+4x+5x+120=180 simplifies to 0=0</LI><LI><B>Cartoon (animation) form</B>: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=simplify_cartoon%28+x%2B4x%2B5x%2B120=180+%29 ALIGN=MIDDLE  ALT=\"simplify_cartoon%28+x%2B4x%2B5x%2B120=180+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR> For tutors: <CODE>simplify_cartoon( x+4x+5x+120=180 )</CODE></LI>\n" );
document.write( "<LI>If you have a website, here's a <A rel=nofollow  rel=nofollow HREF=/services/rendering/simplifier.mpl?expression=x%2B4x%2B5x%2B120=180>link</A> to this solution. </LI>\n" );
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document.write( "<H3  DISABLED_style= \"background-color: #88ccDD; font-weight: bold; margin-top: 0px; margin-bottom: 3px; text-align: center; padding: 2px;\">DETAILED EXPLANATION</H3>\n" );
document.write( "<HR width=50% align=left>Look at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_red%28+x+%29%2Bhighlight_red%28+4%2Ax+%29%2Bhighlight_red%28+5%2Ax+%29%2B120=180 ALIGN=MIDDLE  ALT=\"highlight_red%28+x+%29%2Bhighlight_red%28+4%2Ax+%29%2Bhighlight_red%28+5%2Ax+%29%2B120=180\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR> Eliminated <A  rel=nofollow HREF=/algebra/homework/expressions/>similar terms</A> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_red%28+x+%29 ALIGN=MIDDLE  ALT=\"highlight_red%28+x+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_red%28+4%2Ax+%29 ALIGN=MIDDLE  ALT=\"highlight_red%28+4%2Ax+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_red%28+5%2Ax+%29 ALIGN=MIDDLE  ALT=\"highlight_red%28+5%2Ax+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >  replacing them with  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%28+%281%2B4%2B5%29%2Ax+%29 ALIGN=MIDDLE  ALT=\"highlight_green%28+%281%2B4%2B5%29%2Ax+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>It becomes <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%28+%281%2B4%2B5%29%2Ax+%29%2B120=180& border=1  ALIGN=MIDDLE  ALT=\"highlight_green%28+%281%2B4%2B5%29%2Ax+%29%2B120=180\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "<HR width=50% align=left>Look at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28highlight_red%28+1+%29%2Bhighlight_red%28+4+%29%2Bhighlight_red%28+5+%29%29%2Ax%2B120=180 ALIGN=MIDDLE  ALT=\"%28highlight_red%28+1+%29%2Bhighlight_red%28+4+%29%2Bhighlight_red%28+5+%29%29%2Ax%2B120=180\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR> Added fractions or integers together <BR>It becomes <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28highlight_green%28+10+%29%29%2Ax%2B120=180& border=1  ALIGN=MIDDLE  ALT=\"%28highlight_green%28+10+%29%29%2Ax%2B120=180\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "<HR width=50% align=left>Look at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_red%28+%28highlight_red%28+10+%29%29%2Ax+%29%2B120=180 ALIGN=MIDDLE  ALT=\"highlight_red%28+%28highlight_red%28+10+%29%29%2Ax+%29%2B120=180\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR> Remove unneeded parentheses around factor <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_red%28+10+%29 ALIGN=MIDDLE  ALT=\"highlight_red%28+10+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>It becomes <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%28+10+%29%2Ax%2B120=180& border=1  ALIGN=MIDDLE  ALT=\"highlight_green%28+10+%29%2Ax%2B120=180\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "<HR width=50% align=left>Look at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%2Ax%2B120=highlight_red%28+180+%29 ALIGN=MIDDLE  ALT=\"10%2Ax%2B120=highlight_red%28+180+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR> Moved these terms to the left <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%28+-180+%29 ALIGN=MIDDLE  ALT=\"highlight_green%28+-180+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>It becomes <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%2Ax%2B120-highlight_green%28+180+%29=0& border=1  ALIGN=MIDDLE  ALT=\"10%2Ax%2B120-highlight_green%28+180+%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "<HR width=50% align=left>Look at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%2Ax%2Bhighlight_red%28+120+%29-highlight_red%28+180+%29=0 ALIGN=MIDDLE  ALT=\"10%2Ax%2Bhighlight_red%28+120+%29-highlight_red%28+180+%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR> Added fractions or integers together <BR>It becomes <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%2Ax%2Bhighlight_green%28+-60+%29=0& border=1  ALIGN=MIDDLE  ALT=\"10%2Ax%2Bhighlight_green%28+-60+%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "<HR width=50% align=left>Look at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%2Ax%2Bhighlight_red%28+-60+%29=0 ALIGN=MIDDLE  ALT=\"10%2Ax%2Bhighlight_red%28+-60+%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR> Removed extra sign in front of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-60 ALIGN=MIDDLE  ALT=\"-60\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>It becomes <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%2Ax-highlight_green%28+60+%29=0& border=1  ALIGN=MIDDLE  ALT=\"10%2Ax-highlight_green%28+60+%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "<HR width=50% align=left>Look at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_red%28+10%2Ax-60+%29=0 ALIGN=MIDDLE  ALT=\"highlight_red%28+10%2Ax-60+%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR> Solved <A  rel=nofollow HREF=/algebra/homework/Linear-equations/>linear equation</A> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_red%28+10%2Ax-60=0+%29 ALIGN=MIDDLE  ALT=\"highlight_red%28+10%2Ax-60=0+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > equivalent to  10*x-60  =0 <BR>It becomes <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%28+0+%29=0& border=1  ALIGN=MIDDLE  ALT=\"highlight_green%28+0+%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR><B>Result</B>: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=0& border=2 ALIGN=MIDDLE  ALT=\"0=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<B>This is an <A  rel=nofollow HREF=/algebra/homework/equations/>equation</A>!</B> Solutions: <FONT SIZE=+2><U><B>x=6</B></U></FONT>.<BR><BR><H3  DISABLED_style= \"background-color: #88ccDD; font-weight: bold; margin-top: 0px; margin-bottom: 3px; text-align: center; padding: 2px;\">Universal Simplifier and Solver</H3>\n" );
document.write( "<BR>Done!<BR></TD></TR></TABLE><BR>\n" );
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document.write( "With x=6, then 4x=24 and 5x+120=150.  Note these angles add up to 180 degrees.\r<BR>\n" );
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document.write( "Step 8.  ANSWER:  The three angles are 6 degrees, 24 degrees and 150 degrees.\r<BR>\n" );
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document.write( "For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry. </SPAN>\n" );
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