document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1208873>Question 1208873</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In the triangle shown below, DB = DC, DE=CE and <DAE = 48°. Find the measure of<BR>\n" );
document.write( "<ACB.<BR>\n" );
document.write( "https://ibb.co/48VRX5b </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #847378 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13203)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=847378\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "Strategy:<BR>\n" );
document.write( "(1) Use the given congruent line segments to define variables for the measures of the two pairs of congruent angles in triangles BDC and EDC<BR>\n" );
document.write( "(2) Use those variables to find expressions for the measures of all the other angles in the figure (note some of these will not be used in solving the problem)<BR>\n" );
document.write( "(3) BC and DE are parallel, so angles CBD and EDA are congruent.  Use the expressions for the measures of those two angles to solve the problem<br><BR>\n" );
document.write( "DB = DC, so angles DBC and DCB are congruent.  Let x be the measure of each of those two angles.  That makes the measure of angle BDC 180-2x.<br><BR>\n" );
document.write( "DE = CE, so angles ECD and EDC are congruent.  Let y be the measure of each of those two angles.<br><BR>\n" );
document.write( "The sum of the measures of angles BDC, CDE, and EDA is 180 degrees, so the measure of angle EDA is 2x-y.<br><BR>\n" );
document.write( "DE is parallel to BC, so angles CBD and EDA are congruent.  So<br><BR>\n" );
document.write( "x = 2x-y  -->  y = x.<br><BR>\n" );
document.write( "In triangle ABC, the sum of the measures of the angles is 180 degrees:<br><BR>\n" );
document.write( "x + (x+y) + 48 = 180<BR>\n" );
document.write( "x + (x+x) = 132<BR>\n" );
document.write( "3x = 132<BR>\n" );
document.write( "x = 44<br><BR>\n" );
document.write( "The measure of angle ACB is x+y = 2x = 88.<br><BR>\n" );
document.write( "ANSWER: 88 degrees<br><BR>\n" );
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