PSLEDEFG is a parallelogram, DFH is an equilateral triangle and FG = GH.
- Find ∠DFG.
- Find ∠FGD.
- Find ∠HDE.
(a)
FG = GH
Triangle FGH is an isosceles triangle.
∠GFH
= (180° - 136°) ÷ 2
= 44° ÷ 2
= 22° (Isosceles triangle)
∠DFG
= 60° - 22°
= 38° (Equilateral triangle)
(b)
∠DHG
= 60° - 22°
= 38° (Equilateral triangle)
∠DGH
= 180° - 38° - 22°
= 120° (Angles sum of triangle)
∠DGF
= 360° - 136° - 120°
= 104° (Angles at a point)
∠EDF
= ∠DFG
= 38° (Alternate angles)
∠EDH
= 60° + 38°
= 98°
Answer(s): (a) 38°; (b) 104°; (c) 98°