The figure is not drawn to scale. KLP is an equilateral triangle and NLM is an isosceles triangle. MLK and LNQ are straight lines and MK//QP. ∠PLQ = 90° and ∠NPL = 54°.
- Find ∠MLQ.
- Find ∠LNM.
- Find ∠PNQ.
(a)
∠PLK = 60° (Equilateral triangle KLY)
∠PLQ = 90°
∠NPL = 54°
∠MLQ
= 180° - ∠PLQ - ∠PLK
= 180° - 90° - 60°
= 30° (Angles on a straight line)
(b)
∠LNM
= (180° - ∠MLQ ÷ 2
= (180° - 30°) ÷ 2
= 150° ÷ 2
= 75° (Isosceles triangle)
(c)
∠PNL
= 180° - ∠PLQ - ∠NPL
= 180° - 90° - 54°
= 36°
∠PNQ
= 180° - ∠PNL
= 180° - 36°
= 144° (Angles on a straight line)
Answer(s): (a) 30°; (b) 75°; (c) 144°
