document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1204771>Question 1204771</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In the triangle shown here: https://ibb.co/Ch9FTZT, DB = DC , DE = CE and<BR>\n" );
document.write( "∠DAE = 42°. Find the measure of ∠ACB.\r<BR>\n" );
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document.write( "I understand Mr.Greenstamps posted a solution, but it was a \"Here's a hint, now you solve it!\" But my IQ is far too low to solve it despite all the information he gave. Please help.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #841251 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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=841251\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "DB = DC which makes triangle BDC isosceles.<BR>\n" );
document.write( "It will mean base angles B and C are congruent.<BR>\n" );
document.write( "In other words, angle DBC = angle DCB.<BR>\n" );
document.write( "Let x represent the measure of each base angle.<BR>\n" );
document.write( "The congruent base angles are opposite the congruent sides.\r<BR>\n" );
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document.write( "Because BC is parallel to DE (due to the arrow markers), we know that alternate interior angles BCD and EDC are congruent. <BR>\n" );
document.write( "Both are x.\r<BR>\n" );
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document.write( "Triangle DEC is isosceles since DE = CE. <BR>\n" );
document.write( "The congruent base angles are D and C (aka angle EDC and angle ECD). <BR>\n" );
document.write( "Each of these angles are x.\r<BR>\n" );
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document.write( "Focus on triangle DEC. Use the remote interior angle theorem to find that (angleEDC)+(angleECD) = angleAED<BR>\n" );
document.write( "Or you can use the corresponding angles theorem to see that angle ACB = angle AED.<BR>\n" );
document.write( "This will lead to angle AED = 2x\r<BR>\n" );
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document.write( "Use the corresponding angles theorem to note that angle ADE = angle ABC = x.\r<BR>\n" );
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document.write( "Here's a diagram summarizing all that we found so far<BR>\n" );
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document.write( "From here focus on triangle AED. <BR>\n" );
document.write( "For any triangle, the interior angles <b>always</b> add to 180 degrees.<BR>\n" );
document.write( "A+E+D = 180<BR>\n" );
document.write( "42+2x+x = 180<BR>\n" );
document.write( "I'll let you take over from here.<BR>\n" );
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