∠FDE=∠DFG (alternate angles between parallels DE and GF),
9x+3=14x-27,
30=5x, x=6, ∠FDE=∠DFG=9x+3=14x-27=57º.
The diagonals of a rectangle are the same length and bisect one another. So they form isosceles triangles.
∠HGF=∠HFG=∠DFG because ∆GHF is isosceles.
∠DGH+∠HFG=90º, ∠DGH=90-57=33º.
∆DHG is also isosceles, so ∠GDH=∠DGH=33º.
∠DHG=180-33-33=180-66=114º.