document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=160671>Question 160671</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The measure of one angle of a triangle is twice the measure of a second angle.  The measure of the third angle is 12 less than the sum of the other two.  Find the measures of the anles of the triangle. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #118478 by </B><A HREF=/tutors/aboutme.mpl?userid=gonzo><B>gonzo(654)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=gonzo><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=118478\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> had me going for a while until i remembered that the sum of the internal angles of a triangle are equal to 180 degrees.<BR>\n" );
document.write( "once i remembered that the problem became a lot easier.<BR>\n" );
document.write( "let a, b, and c be the angles of the triangle.<BR>\n" );
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document.write( "let a = 2*b<BR>\n" );
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document.write( "let c = a+b-12<BR>\n" );
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document.write( "the above two statements are given.<BR>\n" );
document.write( "since the sum of the internal angles of a triangle are equal to 180, then we have a third equation to work with which is<BR>\n" );
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document.write( "a + b + c = 180<BR>\n" );
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document.write( "we now have 3 equations for 3 unknowns and we should be able to solve for each of the unknowns.<BR>\n" );
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document.write( "it looks like the easiest thing is to solve for b.  once we find b, the rest should fall into place very nicely.<BR>\n" );
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document.write( "since a = 2*b, we can substitute 2*b for a in the equation a + b + c = 180.<BR>\n" );
document.write( "that equation then becomes 2*b + b + c = 180 which becomes 3*b + c = 180.<BR>\n" );
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document.write( "looking at the equation c = a + b - 12, we solve for b as follows:<BR>\n" );
document.write( "since we know that a = 2 * b, we can substitute 2*b for a and the equation becomes c = 2*b + b - 12 which becomes c = 3*b - 12.<BR>\n" );
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document.write( "the equation we are working with is 3*b + c = 180 which originally started as a + b + c = 180.<BR>\n" );
document.write( "we can substitute 3*b - 12 for c and the equation becomes<BR>\n" );
document.write( "3*b + 3*b - 12 = 180 which becomes 6*b = 192 after adding 12 to both sides and combining like terms.<BR>\n" );
document.write( "dividing both sides of the equation by 6 and we get b = 32 degrees.<BR>\n" );
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document.write( "we have b = 32 degrees.<BR>\n" );
document.write( "we have a = 2 * b so a = 64 degrees.<BR>\n" );
document.write( "we have c = a + b - 12 which becomes c = 32 + 64 - 12 which becomes c = 96 - 12 which becomes c = 84 degrees.<BR>\n" );
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document.write( "substituting in the equation a + b + c = 180, we get 32 + 64 + 84 = 180 which becomes 96 + 84 = 180 which becomes 180 = 180.<BR>\n" );
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document.write( "answer is:<BR>\n" );
document.write( "a = 64 degrees.<BR>\n" );
document.write( "b = 32 degrees.<BR>\n" );
document.write( "c = 84 degrees.<BR>\n" );
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