I'm not sure about this, because i'm not sure if DA and EB are diameters of the circle or not. If they are, then I can answer.
However, if we assume that EB is the diameter...
Arc EB is 180 degrees (the arc that goes through points D and C).
All together, then angle DOC (where O is the center) + angle BOC + angle EOD = 180
We already have 90+52 which is 142
180-142 = 38
So EOD is 38 degrees.
Now, arc AD is 180 degrees (again assuming that AD is the diameter)
So simply do 180-38 which is 142
So arc EA is 142.
You are very welcome!
:P