Answer:
The length of the median is 10, and the measure of the angle ∡A is 68°.
Step-by-step explanation:
Let us start by the median. Recall that the median of a trapezoid is the segment that joins the midpoints of the non-parallel sides. In this case, the median will join the midpoints of the segments DA and CB. The length of the median of a trapezoid can be easily calculated by the formula
[tex] m=\frac{B+b}{2}[/tex]
where [tex]m[/tex] stands for the median, [tex]B[/tex] for the larger of the parallel sides, and [tex]b[/tex] for the shorter one. In this particular case [tex]B=AB[/tex] and [tex]b=DC[/tex]. Thus,
[tex] m=\frac{AB+DC}{2} = \frac{15+5}{2} = 10[/tex].
Finally, recall that one of the main properties of isosceles trapezoid is that the angles adjacent to the parallel sides are equal. Then, as ∡B=68°, we conclude that ∡A is 68°.
