PSLEEFGH is a parallelogram, EGJ is an equilateral triangle and GH = HJ.
- Find ∠EGH.
- Find ∠GHE.
- Find ∠JEF.
(a)
GH = HJ
Triangle GHJ is an isosceles triangle.
∠HGJ
= (180° - 144°) ÷ 2
= 36° ÷ 2
= 18° (Isosceles triangle)
∠EGH
= 60° - 18°
= 42° (Equilateral triangle)
(b)
∠EJH
= 60° - 18°
= 42° (Equilateral triangle)
∠EHJ
= 180° - 42° - 18°
= 120° (Angles sum of triangle)
∠EHG
= 360° - 144° - 120°
= 96° (Angles at a point)
∠FEG
= ∠EGH
= 42° (Alternate angles)
∠FEJ
= 60° + 42°
= 102°
Answer(s): (a) 42°; (b) 96°; (c) 102°