document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=708891>Question 708891</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi! I was wondering if I have a triangle where two of the angles are 60 and the third angle is y and one side is labled 4x how would I find the variables? It also says the perimeter is 54 too.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #436301 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=436301\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> All 3 angles in a triangle add up to 180 degrees, so\r<BR>\n" );
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document.write( "60+60+y = 180\r<BR>\n" );
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document.write( "120 + y = 180\r<BR>\n" );
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document.write( "y = 180 - 120\r<BR>\n" );
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document.write( "y = 60\r<BR>\n" );
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document.write( "So the third angle is 60\r<BR>\n" );
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document.write( "Since each angle is 60, we have an equilateral triangle. So we have 3 sides equal to 4x\r<BR>\n" );
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document.write( "They add to the perimeter of 54, which means\r<BR>\n" );
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document.write( "4x+4x+4x = 54\r<BR>\n" );
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document.write( "12x = 54\r<BR>\n" );
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document.write( "x = 54/12\r<BR>\n" );
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document.write( "x = 27/6\r<BR>\n" );
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document.write( "x = 9/2\r<BR>\n" );
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document.write( "x = 4.5\r<BR>\n" );
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document.write( "So in the end, x = 4.5 and y = 60\r<BR>\n" );
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document.write( "Because x = 4.5, each side is therefore 4.5*4 = 18 units long. </SPAN>\n" );
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