Well, with enough hints I think I finally figured it out.
We know that triangle FHE is equilateral so FE=HE=FH and angle FEH is 60*.
We also know that DF and DH are equal because triangle DFH is isosceles .
So triangles DHE and DFE are congruent, which means angle FED and DEH are equal. The sum of FED and DEH is equal to FEH = 60*. So angle DEH is 30*.
I see, said the blind man as he picked up his hammer and saw.