A E-Z Problem with Trapezoid

Extend $CA$ and $DB$ to meet at $G$ . Since $\angle C + \angle D = 90^\circ$ , then $\angle G = 90^\circ$ and $\triangle CDG$ is inscribed in a semicircle with $CD$ as the diameter. Since $F$ is the midpoint of $CD$ , it is the center of the semicircle and $FG = CF=FD = 5.5$ .

As $\triangle GAE$ and $\triangle GCF$ are similar, then we have $\dfrac {GE}{GF} = \dfrac {AE}{CF} = \dfrac {2.5}{5.5} \implies GE = \dfrac {2.5}{5.5} \times 5.5 = 2.5$ and $EF = GF-GE = 5.5-2.5 = \boxed 3$ .

I graphed it on GeoGebra!

Clearly from the diagram, EF=3

By the way, I found that other options will make the sum of $∠D + ∠C$ greater than $90 \degree$ .