Final answer:
In an isosceles trapezoid with midpoints V and Y on the legs, if FE=18 and VY=28, then CD=18. The measure of angle D in the trapezoid is found by subtracting the measures of angles F and E from 360 and then halving the result since angles at C and D are congruent.
Step-by-step explanation:
The student has asked two different questions related to a trapezoid named FEDC, where V and Y are the midpoints of the non-parallel sides. For the first part, assuming that FEDC is an isosceles trapezoid (which is a typical assumption when dealing with midpoints in trapezoids), we can infer that CD is also equal to FE, thus CD also measures 18 units.
For the second part, the sum of angles in any quadrilateral is 360 degrees. Since we have m°F = 140 degrees and m°E = 125 degrees, we subtract these from 360 to find the sum of angles D and C. After that, since V and Y are midpoints, angles at V and Y are congruent to angles at F and E respectively, which makes angles at C and D congruent as well. Therefore, m°C + m°D = 360 - (m°F + m°E), and m°D can be found by halving the resulting sum.