The figure is not drawn to scale. GHKL is a parallelogram. ∠LGO is 54° and ∠KHJ is 24°. GHJ is an isosceles triangle and GH = HJ.
- Find ∠OJH.
- Find ∠GLK.
(a)
∠HOG = 54° (Alternate angles, GL//HK)
∠HOJ
= 180° - 54°
= 126° (Angles on a straight line)
∠OJH
= 180° - 126° - 24°
= 30° (Angles sum of triangle)
(b)
∠HGO = 30° (Isosceles triangle GHJ)
∠GLK
= 180° - 54° - 30°
= 96° (Interior angles, GH//LK)
Answer(s): (a) 30°; (b) 96°