document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=896311>Question 896311</A>: <I><SPAN STYLE=\"word-break: break-all;\"> ABDE is a square section and BDC is an equilateral triangle with C outside the square. Compute the value of angle ACE. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #543391 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=543391\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \r<BR>\n" );
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document.write( "see the following diagram.<BR>\n" );
document.write( "further comments are below the diagram.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2014/083003.jpg\" alt=\"$$$\" </>\r<BR>\n" );
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document.write( "your equilateral triangle is BCD.<BR>\n" );
document.write( "since it's an equilateral triangle, all angles are equal to 60 degrees.<BR>\n" );
document.write( "you draw a line from A to C and from E to C.<BR>\n" );
document.write( "this forms 2 isosceles triangles of ABC and EDC.<BR>\n" );
document.write( "the congruent legs of triangle ABC are:<BR>\n" );
document.write( "AB and BC<BR>\n" );
document.write( "the congruent legs of triangle EDC are:<BR>\n" );
document.write( "ED and DC<BR>\n" );
document.write( "the angles opposite these congruent legs are equal.<BR>\n" );
document.write( "the angles that are equal for triangle ABC are:<BR>\n" );
document.write( "angle BAC and angle BCA<BR>\n" );
document.write( "the angles that are equal for triangle EDC are:<BR>\n" );
document.write( "angle DEC and angle DCE<BR>\n" );
document.write( "angle ABC is composed of angle ABD which is 90 degrees and angle CBD which is 60 degrees.   angle ABC is therefore equal to 150 degrees because 90 + 60 = 150.<BR>\n" );
document.write( "since the sum of the angles of a triangle is equal to 180 degrees, this means that angles BAC and BCA must be equal to 30 degrees in total because angle ABC is equal to 150 degrees.<BR>\n" );
document.write( "since those angles are equal, then each of them must be equal to 15 degrees.<BR>\n" );
document.write( "similarly angles DEC and DCE must each be equal to 15 degrees also.<BR>\n" );
document.write( "the angle in question is angle ACE which is the third part of angle C which is equal to 60 degrees.<BR>\n" );
document.write( "the first part is angle BCA which is equal to 15 degrees.<BR>\n" );
document.write( "the second part is angle DCE which is equal to 15 degrees.<BR>\n" );
document.write( "the third part is angle ACE which has to be equal to 30 degrees since 60 - 15 - 15 = 30.\r<BR>\n" );
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document.write( "that's your answer.<BR>\n" );
document.write( "angle ACE is equal to 30 degrees.<BR>\n" );
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