PSLELMNP is a parallelogram, LNQ is an equilateral triangle and NP = PQ.
- Find ∠LNP.
- Find ∠NPL.
- Find ∠QLM.
(a)
NP = PQ
Triangle NPQ is an isosceles triangle.
∠PNQ
= (180° - 140°) ÷ 2
= 40° ÷ 2
= 20° (Isosceles triangle)
∠LNP
= 60° - 20°
= 40° (Equilateral triangle)
(b)
∠LQP
= 60° - 20°
= 40° (Equilateral triangle)
∠LPQ
= 180° - 40° - 20°
= 120° (Angles sum of triangle)
∠LPN
= 360° - 140° - 120°
= 100° (Angles at a point)
∠MLN
= ∠LNP
= 40° (Alternate angles)
∠MLQ
= 60° + 40°
= 100°
Answer(s): (a) 40°; (b) 100°; (c) 100°
