The figure is not drawn to scale. GHL is an equilateral triangle and KHJ is an isosceles triangle. JHG and HKM are straight lines and JG//ML. ∠LHM = 90° and ∠KLH = 59°.
- Find ∠JHM.
- Find ∠HKJ.
- Find ∠LKM.
(a)
∠LHG = 60° (Equilateral triangle GHY)
∠LHM = 90°
∠KLH = 59°
∠JHM
= 180° - ∠LHM - ∠LHG
= 180° - 90° - 60°
= 30° (Angles on a straight line)
(b)
∠HKJ
= (180° - ∠JHM ÷ 2
= (180° - 30°) ÷ 2
= 150° ÷ 2
= 75° (Isosceles triangle)
(c)
∠LKH
= 180° - ∠LHM - ∠KLH
= 180° - 90° - 59°
= 31°
∠LKM
= 180° - ∠LKH
= 180° - 31°
= 149° (Angles on a straight line)
Answer(s): (a) 30°; (b) 75°; (c) 149°
