document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1209478>Question 1209478</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In triangle ABC, DE is parallel to BC and AD = DE = BE.<BR>\n" );
document.write( "If BE is the angle bisector of angle CBA, then find the measure of angle ACB.\r<BR>\n" );
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document.write( "Link to the graph: https://ibb.co/h9RJzZR </SPAN>\n" );
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document.write( "Since BE bisects angle CBA, let x be the measure of each of angles CBE and EBD.<br><BR>\n" );
document.write( "In triangle DEB, DE = BE, so the measure of angle BDE is also x.<br><BR>\n" );
document.write( "That makes the measure of angle EDA 180-x.<br><BR>\n" );
document.write( "But DE and BC are parallel, so angles EDA and CBA are congruent.<br><BR>\n" );
document.write( "2x = 180-x<BR>\n" );
document.write( "3x = 180<BR>\n" );
document.write( "x = 60<br><BR>\n" );
document.write( "In triangle EDA, AD = DE, so angles DAE and DEA are congruent.  Then, since the measure of angle EDA is 180-x=120, the measure of each of angles DAE and DEA is x/2 = 30.<br><BR>\n" );
document.write( "And again DE and BC are parallel, so the measure of angle ACB is also 30.<br><BR>\n" );
document.write( "ANSWER: 30 degrees<br><BR>\n" );
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