The figure is not drawn to scale. EFJ is an equilateral triangle and HFG is an isosceles triangle. GFE and FHK are straight lines and GE//KJ. ∠JFK = 90° and ∠HJF = 59°.
- Find ∠GFK.
- Find ∠FHG.
- Find ∠JHK.
(a)
∠JFE = 60° (Equilateral triangle EFY)
∠JFK = 90°
∠HJF = 59°
∠GFK
= 180° - ∠JFK - ∠JFE
= 180° - 90° - 60°
= 30° (Angles on a straight line)
(b)
∠FHG
= (180° - ∠GFK ÷ 2
= (180° - 30°) ÷ 2
= 150° ÷ 2
= 75° (Isosceles triangle)
(c)
∠JHF
= 180° - ∠JFK - ∠HJF
= 180° - 90° - 59°
= 31°
∠JHK
= 180° - ∠JHF
= 180° - 31°
= 149° (Angles on a straight line)
Answer(s): (a) 30°; (b) 75°; (c) 149°
