The figure is not drawn to scale. FGJK is a parallelogram. ∠KFO is 54° and ∠JGH is 24°. FGH is an isosceles triangle and FG = GH.
- Find ∠OHG.
- Find ∠FKJ.
(a)
∠GOF = 54° (Alternate angles, FK//GJ)
∠GOH
= 180° - 54°
= 126° (Angles on a straight line)
∠OHG
= 180° - 126° - 24°
= 30° (Angles sum of triangle)
(b)
∠GFO = 30° (Isosceles triangle FGH)
∠FKJ
= 180° - 54° - 30°
= 96° (Interior angles, FG//KJ)
Answer(s): (a) 30°; (b) 96°