DEFG is a rectangle. Find m<DHG.

Question

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Answer 1

∠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.