Take the midpoint o of DE. Because AF is perpendicular to BC and AD is parallel to BC, the angle EAD=90 degrees.

In Rt triangle ADE, DE=2AO, because DE=2AB, AB=AO,

So angle ABO= angle AOB.

Because AO=OD. So angel ·OAD = angel oder,

So angle AOB= angle OAD+ angle ODA=2 angle ODA.

Because AD is parallel to DC, angle DBC= angle ODA= half angle AOB= half angle ABO.

So the intersection ABO=2 angle OBC. So the angle OBC= one third angle ABC=25 degrees.

So the angle ODA= the angle OBC=25 degrees.

So AED angle = 180-90-25=75 degrees.

(I don't know if there is no picture, right)