The figure is not drawn to scale. FGK is an equilateral triangle and JGH is an isosceles triangle. HGF and GJL are straight lines and HF//LK. ∠KGL = 90° and ∠JKG = 52°.
- Find ∠HGL.
- Find ∠GJH.
- Find ∠KJL.
(a)
∠KGF = 60° (Equilateral triangle FGY)
∠KGL = 90°
∠JKG = 52°
∠HGL
= 180° - ∠KGL - ∠KGF
= 180° - 90° - 60°
= 30° (Angles on a straight line)
(b)
∠GJH
= (180° - ∠HGL ÷ 2
= (180° - 30°) ÷ 2
= 150° ÷ 2
= 75° (Isosceles triangle)
(c)
∠KJG
= 180° - ∠KGL - ∠JKG
= 180° - 90° - 52°
= 38°
∠KJL
= 180° - ∠KJG
= 180° - 38°
= 142° (Angles on a straight line)
Answer(s): (a) 30°; (b) 75°; (c) 142°
