SOLUTION: Trapezoid ACDF is isosceles with mid-segment line BE. If measure angle C equals 177•, find measure angle A and measure angle D.

Here it is drawn with the actual angles.  It's very short and wide.


The (green) mid-segment BE is not involved in the problem at all.  So let's erase it,
since it just gets in the way:



Since the trapezoid is isosceles, angle A also has measure 177°.
Also angle D and angle F have the same measure.

A trapezoid is a quadrilateral, so the sum of the interior angles
of a quadrilateral is 360°, So angles D and F together have sum of
measures 360°-2·177° = 6°.  Therefore angles D and F have measure
which is half of that or 3°.





Edwin