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° - 140°) ÷ 2
= 40° ÷ 2
= 20° (Isosceles triangle)
∠EGH
= 60° - 20°
= 40° (Equilateral triangle)
(b)
∠EJH
= 60° - 20°
= 40° (Equilateral triangle)
∠EHJ
= 180° - 40° - 20°
= 120° (Angles sum of triangle)
∠EHG
= 360° - 140° - 120°
= 100° (Angles at a point)
∠FEG
= ∠EGH
= 40° (Alternate angles)
∠FEJ
= 60° + 40°
= 100°
Answer(s): (a) 40°; (b) 100°; (c) 100°
