The figure is not drawn to scale. HJM is an equilateral triangle and LJK is an isosceles triangle. KJH and JLN are straight lines and KH//NM. ∠MJN = 90° and ∠LMJ = 56°.
- Find ∠KJN.
- Find ∠JLK.
- Find ∠MLN.
(a)
∠MJH = 60° (Equilateral triangle HJY)
∠MJN = 90°
∠LMJ = 56°
∠KJN
= 180° - ∠MJN - ∠MJH
= 180° - 90° - 60°
= 30° (Angles on a straight line)
(b)
∠JLK
= (180° - ∠KJN ÷ 2
= (180° - 30°) ÷ 2
= 150° ÷ 2
= 75° (Isosceles triangle)
(c)
∠MLJ
= 180° - ∠MJN - ∠LMJ
= 180° - 90° - 56°
= 34°
∠MLN
= 180° - ∠MLJ
= 180° - 34°
= 146° (Angles on a straight line)
Answer(s): (a) 30°; (b) 75°; (c) 146°
