I have no clue if this is correct, but I'll give it a shot:
We know Angle A is 34 degrees, and we know angle E is a right angle, making Angle E 90 degrees.
A triangle can only be 180 degrees in total, so 180 - (34+90) = 55.
Angle B is 55 degrees. Angle E is 90 degrees.
90 + 55 = 145.
This means that Angle D is 180-145 = 35 degrees.
Angle D is 35 Degrees.
Though I may be incorrect because of the internal/external angles... idk tho