document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=341992>Question 341992</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If line segment BD is the angle bisector of angle ABC, line segment BE is the angle bisector of angle ABD, and the measurement of angle DBC= 24 degrees, what is the measurement of angle EBC? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #244844 by </B><A HREF=/tutors/aboutme.mpl?userid=Edwin+McCravy><B>Edwin McCravy(20059)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Edwin+McCravy><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=Edwin+McCravy><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=244844\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> `<BR>\n" );
document.write( "If line segment BD is the angle bisector of angle ABC,<BR>\n" );
document.write( "`<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28400%2C400%2C-.5%2C2.5%2C-1.5%2C1.5%2C%0D%0A%0D%0Ared%28arc%280%2C0%2C2%2C-2%2C0%2C24%29%29%2C+red%28arc%280%2C0%2C1.8%2C-1.8%2C-24%2C0%29%29%2C%0D%0Alocate%280%2C0%2CB%29%2C+locate%282cos%2824%2Api%2F180%29%2C0%2C+D%29%2C%0D%0Aline%280%2C0%2C2cos%2824%2Api%2F180%29%2C0%29%2C%0D%0Aline%280%2C0%2C2cos%2824%2Api%2F180%29%2C2sin%2824%2Api%2F180%29%29%2C%0D%0Alocate%282cos%2824%2Api%2F180%29%2C-2sin%2824%2Api%2F180%29%2CC%29%2C%0D%0Alocate%282cos%2824%2Api%2F180%29%2C2sin%2824%2Api%2F180%29%2CA%29%2C%0D%0Aline%280%2C0%2C2cos%2824%2Api%2F180%29%2C-2sin%2824%2Api%2F180%29%29++%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "`<BR>\n" );
document.write( "line segment BE is the angle bisector of angle ABD,<BR>\n" );
document.write( "`<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28400%2C400%2C-.5%2C2.5%2C-1.5%2C1.5%2C%0D%0Ared%28arc%280%2C0%2C2%2C-2%2C0%2C24%29%29%2C+red%28arc%280%2C0%2C1.8%2C-1.8%2C-24%2C0%29%29%2C%0D%0Alocate%280%2C0%2CB%29%2C+locate%282cos%2824%2Api%2F180%29%2C0%2C+D%29%2C%0D%0Agreen%28arc%280%2C0%2C3%2C-3%2C0%2C12%29%29%2C+green%28arc%280%2C0%2C2.8%2C-2.8%2C12%2C24%29%29%2C%0D%0Aline%280%2C0%2C2cos%2812%2Api%2F180%29%2C2sin%2812%2Api%2F180%29%29%2C%0D%0Alocate%282cos%2812%2Api%2F180%29%2C2sin%2812%2Api%2F180%29%2CE%29%2C%0D%0Aline%280%2C0%2C2cos%2824%2Api%2F180%29%2C0%29%2C%0D%0Aline%280%2C0%2C2cos%2824%2Api%2F180%29%2C2sin%2824%2Api%2F180%29%29%2C%0D%0Alocate%282cos%2824%2Api%2F180%29%2C-2sin%2824%2Api%2F180%29%2CC%29%2C%0D%0Alocate%282cos%2824%2Api%2F180%29%2C2sin%2824%2Api%2F180%29%2CA%29%2C%0D%0Aline%280%2C0%2C2cos%2824%2Api%2F180%29%2C-2sin%2824%2Api%2F180%29%29++%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "`<BR>\n" );
document.write( "and the measurement of angle DBC= 24 degrees,<BR>\n" );
document.write( "`<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28400%2C400%2C-.5%2C2.5%2C-1.5%2C1.5%2C%0D%0Ared%28arc%280%2C0%2C2%2C-2%2C0%2C24%29%29%2C+red%28arc%280%2C0%2C1.8%2C-1.8%2C-24%2C0%29%29%2C%0D%0Alocate%280%2C0%2CB%29%2C+locate%282cos%2824%2Api%2F180%29%2C0%2C+D%29%2C%0D%0Agreen%28arc%280%2C0%2C3%2C-3%2C0%2C12%29%29%2C+green%28arc%280%2C0%2C2.8%2C-2.8%2C12%2C24%29%29%2C%0D%0Aline%280%2C0%2C2cos%2812%2Api%2F180%29%2C2sin%2812%2Api%2F180%29%29%2C%0D%0Alocate%28.6%2C-.1%2C%2224%B0%22%29%2C%0D%0Alocate%282cos%2812%2Api%2F180%29%2C2sin%2812%2Api%2F180%29%2CE%29%2C%0D%0Aline%280%2C0%2C2cos%2824%2Api%2F180%29%2C0%29%2C%0D%0Aline%280%2C0%2C2cos%2824%2Api%2F180%29%2C2sin%2824%2Api%2F180%29%29%2C%0D%0Alocate%282cos%2824%2Api%2F180%29%2C-2sin%2824%2Api%2F180%29%2CC%29%2C%0D%0Alocate%282cos%2824%2Api%2F180%29%2C2sin%2824%2Api%2F180%29%2CA%29%2C%0D%0Aline%280%2C0%2C2cos%2824%2Api%2F180%29%2C-2sin%2824%2Api%2F180%29%29++%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\"><b>\r\n" );
document.write( "Since line segment BD is the bisector of angle ABC, then the measure\r\n" );
document.write( "of angle ABD is also 24°\r\n" );
document.write( "\r\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28400%2C400%2C-.5%2C2.5%2C-1.5%2C1.5%2C%0D%0Ared%28arc%280%2C0%2C2%2C-2%2C0%2C24%29%29%2C+red%28arc%280%2C0%2C1.8%2C-1.8%2C-24%2C0%29%29%2C%0D%0Alocate%280%2C0%2CB%29%2C+locate%282cos%2824%2Api%2F180%29%2C0%2C+D%29%2C%0D%0Agreen%28arc%280%2C0%2C3%2C-3%2C0%2C12%29%29%2C+green%28arc%280%2C0%2C2.8%2C-2.8%2C12%2C24%29%29%2C%0D%0Aline%280%2C0%2C2cos%2812%2Api%2F180%29%2C2sin%2812%2Api%2F180%29%29%2C%0D%0Alocate%28.6%2C-.1%2C%2224%B0%22%29%2C+locate%28.6%2C.2%2C%2224%B0%22%29%2C%0D%0Alocate%282cos%2812%2Api%2F180%29%2C2sin%2812%2Api%2F180%29%2CE%29%2C+%0D%0Aline%280%2C0%2C2cos%2824%2Api%2F180%29%2C0%29%2C%0D%0Aline%280%2C0%2C2cos%2824%2Api%2F180%29%2C2sin%2824%2Api%2F180%29%29%2C%0D%0Alocate%282cos%2824%2Api%2F180%29%2C-2sin%2824%2Api%2F180%29%2CC%29%2C%0D%0Alocate%282cos%2824%2Api%2F180%29%2C2sin%2824%2Api%2F180%29%2CA%29%2C%0D%0Aline%280%2C0%2C2cos%2824%2Api%2F180%29%2C-2sin%2824%2Api%2F180%29%29++%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r\n" );
document.write( "\r\n" );
document.write( "and since line segment BE is the angle bisector of angle ABD,\r\n" );
document.write( "Both angle ABE and EBD have measure 12° each.\r\n" );
document.write( "\r\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28400%2C400%2C-.5%2C2.5%2C-1.5%2C1.5%2C%0D%0Ared%28arc%280%2C0%2C2%2C-2%2C0%2C24%29%29%2C+red%28arc%280%2C0%2C1.8%2C-1.8%2C-24%2C0%29%29%2C%0D%0Alocate%280%2C0%2CB%29%2C+locate%282cos%2824%2Api%2F180%29%2C0%2C+D%29%2C%0D%0Agreen%28arc%280%2C0%2C3%2C-3%2C0%2C12%29%29%2C+green%28arc%280%2C0%2C2.8%2C-2.8%2C12%2C24%29%29%2C%0D%0Aline%280%2C0%2C2cos%2812%2Api%2F180%29%2C2sin%2812%2Api%2F180%29%29%2C%0D%0Alocate%28.6%2C-.1%2C%2224%B0%22%29%2C+locate%28.6%2C.2%2C%2224%B0%22%29%2C%0D%0Alocate%282cos%2812%2Api%2F180%29%2C2sin%2812%2Api%2F180%29%2CE%29%2C+%0D%0Aline%280%2C0%2C2cos%2824%2Api%2F180%29%2C0%29%2C%0D%0Aline%280%2C0%2C2cos%2824%2Api%2F180%29%2C2sin%2824%2Api%2F180%29%29%2C%0D%0Alocate%282cos%2824%2Api%2F180%29%2C-2sin%2824%2Api%2F180%29%2CC%29%2C%0D%0Alocate%282cos%2824%2Api%2F180%29%2C2sin%2824%2Api%2F180%29%2CA%29%2C%0D%0Aline%280%2C0%2C2cos%2824%2Api%2F180%29%2C-2sin%2824%2Api%2F180%29%29%2C%0D%0Alocate%281.6%2C.25%2C%2212%B0%22%29%2C+locate%281.4%2C.5%2C%2212%B0%22%29++%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r\n" );
document.write( "\r\n" );
document.write( "Then the angle EBC, indicated by the double blue arcs below,\r\n" );
document.write( "has measure equal to sum of the measures of its parts,\r\n" );
document.write( "angle EBD and angle DBC.  The measure of angle EBD is\r\n" );
document.write( "12° and the measure of angle DBC is 24°, and their sum\r\n" );
document.write( "is 12°+24° or 36°. So angle EBC has measure 36°.\r\n" );
document.write( " \r\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28400%2C400%2C-.5%2C2.5%2C-1.5%2C1.5%2C%0D%0Ared%28arc%280%2C0%2C2%2C-2%2C0%2C24%29%29%2C+red%28arc%280%2C0%2C1.8%2C-1.8%2C-24%2C0%29%29%2C%0D%0Alocate%280%2C0%2CB%29%2C+locate%282cos%2824%2Api%2F180%29%2C0%2C+D%29%2C%0D%0Agreen%28arc%280%2C0%2C3%2C-3%2C0%2C12%29%29%2C+green%28arc%280%2C0%2C2.8%2C-2.8%2C12%2C24%29%29%2C%0D%0Aline%280%2C0%2C2cos%2812%2Api%2F180%29%2C2sin%2812%2Api%2F180%29%29%2C%0D%0Alocate%28.6%2C-.1%2C%2224%B0%22%29%2C+locate%28.6%2C.2%2C%2224%B0%22%29%2C%0D%0Alocate%282cos%2812%2Api%2F180%29%2C2sin%2812%2Api%2F180%29%2CE%29%2C+%0D%0Aline%280%2C0%2C2cos%2824%2Api%2F180%29%2C0%29%2C%0D%0Aline%280%2C0%2C2cos%2824%2Api%2F180%29%2C2sin%2824%2Api%2F180%29%29%2C%0D%0Alocate%282cos%2824%2Api%2F180%29%2C-2sin%2824%2Api%2F180%29%2CC%29%2C%0D%0Alocate%282cos%2824%2Api%2F180%29%2C2sin%2824%2Api%2F180%29%2CA%29%2C%0D%0Aline%280%2C0%2C2cos%2824%2Api%2F180%29%2C-2sin%2824%2Api%2F180%29%29%2C%0D%0Alocate%281.6%2C.25%2C%2212%B0%22%29%2C+locate%281.4%2C.5%2C%2212%B0%22%29%2C%0D%0Ablue%28arc%280%2C0%2C2.3%2C-2.3%2C-24%2C12%29%29%2C%0D%0Ablue%28arc%280%2C0%2C2.2%2C-2.2%2C-24%2C12%29%29%2C%0D%0Ablue%28locate%281.1%2C-.1%2C%2236%B0%22%29%29++%0D%0A%0D%0A%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r\n" );
document.write( "\r\n" );
document.write( "Edwin</PRE></b> </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );