document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1023440>Question 1023440</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Point X is on side Line AC of Triangle ABC such that angle AXB =angle ABX, and angle ABC - angle ACB = 39. Find angle XBC in degrees. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #638976 by </B><A HREF=/tutors/aboutme.mpl?userid=simranb><B>simranb(63)</B></A><img src=\"/images/stars/stars-08.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=simranb><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=simranb><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=638976\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Given angle AXB =angle ABX  and angle ABC - angle ACB = 39<BR>\n" );
document.write( "Let angle AXB and angle ABX be 'a degrees'. <BR>\n" );
document.write( "Consider the triangle AXB,<BR>\n" );
document.write( " angle AXB + angle ABX + angle BAX = 180 ( sum of all three angles of a triangle is 180)<BR>\n" );
document.write( "     a + a + angle BAX = 180<BR>\n" );
document.write( "             angle BAX = 180-2a<BR>\n" );
document.write( "Let angle ABC be 'x' and angle BCA be 'y'.<BR>\n" );
document.write( "Consider triangle ABC<BR>\n" );
document.write( "    angle ABC + angle BCA + angle BAC = 180<BR>\n" );
document.write( "         x + y + (180-2a) = 180 ( angle BAC is same as the angle BAX)<BR>\n" );
document.write( "          x+y-2a=0<BR>\n" );
document.write( "           x+y = 2a ------------ Eq 1<BR>\n" );
document.write( "It is given that, angle ABC - angle ACB = 39<BR>\n" );
document.write( "   so, x-y = 39 --------------Eq 2<BR>\n" );
document.write( "Adding Equations 1 and 2 gives,<BR>\n" );
document.write( "          2x = 39+2a<BR>\n" );
document.write( "           x = (39+2a)/2<BR>\n" );
document.write( "You must note that angle XBC is angle ABC- angle ABX, that is nothing but <BR>\n" );
document.write( "angle XBC = x-a <BR>\n" );
document.write( "          = (39+2a)/2 - a<BR>\n" );
document.write( "          = (39+2a-2a)/2<BR>\n" );
document.write( "          =39/2<BR>\n" );
document.write( "          = 19.5 degrees\r<BR>\n" );
document.write( "\n" );
document.write( "Hope this helps!\r<BR>\n" );
document.write( "\n" );
document.write( "Cheers!<BR>\n" );
document.write( "Simran Bhuria </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );