document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=28822>Question 28822</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The measure of the second angle of a triangle is 12 degrees greater then three times the first angle. The measure of the third angle is 6 degrees less than twice the measure of the second angle. What are the measures of the three angles?\r<BR>\n" );
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document.write( "Thanks so much!!! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #15722 by </B><A HREF=/tutors/aboutme.mpl?userid=sdmmadam@yahoo.com><B>sdmmadam@yahoo.com(530)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=sdmmadam@yahoo.com><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=15722\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The measure of the second angle of a triangle is 12 degrees greater then three times the first angle. The measure of the third angle is 6 degrees less than twice the measure of the second angle. What are the measures of the three angles?\r<BR>\n" );
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document.write( "Let the first angle be A degrees, <BR>\n" );
document.write( "the second angle be B degrees and <BR>\n" );
document.write( "the third angle be C degrees.<BR>\n" );
document.write( "The second angle is 12 degrees greater than three times first angle.<BR>\n" );
document.write( "B is 12 more than 3A<BR>\n" );
document.write( "That is B= 3A+12 ----(1)<BR>\n" );
document.write( "The third angle is 6 less than twice the second angle.<BR>\n" );
document.write( "C is 6 less than 2B<BR>\n" );
document.write( "C=2B-6 ----(2)<BR>\n" );
document.write( "A,B and C being the angles of a triangle ABC,<BR>\n" );
document.write( "we have A + B + C = 180 degrees.  ----(*)<BR>\n" );
document.write( "Using (1) and (2) in (*)<BR>\n" );
document.write( "A +(3A+12)+(2B-6) =180<BR>\n" );
document.write( "A+3A +12-6+2B=180<BR>\n" );
document.write( "4A+6+2B=180<BR>\n" );
document.write( "4A+2B= 180-6<BR>\n" );
document.write( "4A+2B= 174<BR>\n" );
document.write( "4A+ 2(3A+12) =174 using (1) and substituting for B in terms of A<BR>\n" );
document.write( "4A+6A+24 =174<BR>\n" );
document.write( "10A=174-24<BR>\n" );
document.write( "10A = 150<BR>\n" );
document.write( "A = 150/10 = 15<BR>\n" );
document.write( "A= 15 in (1),then B= 3A+12 = 3X15+12 = 45+12 =57<BR>\n" );
document.write( "Putting B= 57 in (2), <BR>\n" );
document.write( "C=2B-6 = 2X57-6 = 114-6 = 108<BR>\n" );
document.write( "Therefore the angles are 15 deg, 57 deg and 108 deg respectively.<BR>\n" );
document.write( "Verification: Obviously they are adding up to 180 beautifully. Good\r<BR>\n" );
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