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° - 134°) ÷ 2
= 46° ÷ 2
= 23° (Isosceles triangle)
∠GJK
= 60° - 23°
= 37° (Equilateral triangle)
(b)
∠GLK
= 60° - 23°
= 37° (Equilateral triangle)
∠GKL
= 180° - 37° - 23°
= 120° (Angles sum of triangle)
∠GKJ
= 360° - 134° - 120°
= 106° (Angles at a point)
∠HGJ
= ∠GJK
= 37° (Alternate angles)
∠HGL
= 60° + 37°
= 97°
Answer(s): (a) 37°; (b) 106°; (c) 97°