PSLEGHJK is a parallelogram, GJL is an equilateral triangle and JK = KL.
- Find ∠GJK.
- Find ∠JKG.
- Find ∠LGH.
(a)
JK = KL
Triangle JKL is an isosceles triangle.
∠KJL
= (180° - 146°) ÷ 2
= 34° ÷ 2
= 17° (Isosceles triangle)
∠GJK
= 60° - 17°
= 43° (Equilateral triangle)
(b)
∠GLK
= 60° - 17°
= 43° (Equilateral triangle)
∠GKL
= 180° - 43° - 17°
= 120° (Angles sum of triangle)
∠GKJ
= 360° - 146° - 120°
= 94° (Angles at a point)
∠HGJ
= ∠GJK
= 43° (Alternate angles)
∠HGL
= 60° + 43°
= 103°
Answer(s): (a) 43°; (b) 94°; (c) 103°