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° - 138°) ÷ 2
= 42° ÷ 2
= 21° (Isosceles triangle)
∠DFG
= 60° - 21°
= 39° (Equilateral triangle)
(b)
∠DHG
= 60° - 21°
= 39° (Equilateral triangle)
∠DGH
= 180° - 39° - 21°
= 120° (Angles sum of triangle)
∠DGF
= 360° - 138° - 120°
= 102° (Angles at a point)
∠EDF
= ∠DFG
= 39° (Alternate angles)
∠EDH
= 60° + 39°
= 99°
Answer(s): (a) 39°; (b) 102°; (c) 99°
