Question 1199998

In the diagram, Angle A = 40° while BD and CD are the bisectors of
angles EBC and FCB respectively. Find the measure of angle D. 

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Thanks!
<pre><font color = blue><font size = 4><b>Let &#8737ACB be x<sup>o</sup>
Then &#8737ABC = 180 - (40 + x) = (140 - x)<sup>o</sup>
Therefore, &#8737FCB = (180 - x)<sup>o</sup>, and &#8737EBC = 180 - (140 - x) = (40 + x)<sup>o</sup>
As BD bisects &#8737EBC, &#8737DBC = {{{matrix(1,3, (40 + x)/2, "or", 20 + x/2)}}} 
Likewise, since DC bisects &#8737FCB, &#8737DCB = {{{matrix(1,3, (180 - x)/2, "or", 90 - x/2)}}} 
Thus &#8737D = {{{highlight_green(matrix(1,5, 180 - (20 + x/2 + 90 - x/2), "=", 180 - 110, "=", highlight(70^o)))}}}</font></font></b></pre>