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° - 146°) ÷ 2
= 34° ÷ 2
= 17° (Isosceles triangle)
∠LNP
= 60° - 17°
= 43° (Equilateral triangle)
(b)
∠LQP
= 60° - 17°
= 43° (Equilateral triangle)
∠LPQ
= 180° - 43° - 17°
= 120° (Angles sum of triangle)
∠LPN
= 360° - 146° - 120°
= 94° (Angles at a point)
∠MLN
= ∠LNP
= 43° (Alternate angles)
∠MLQ
= 60° + 43°
= 103°
Answer(s): (a) 43°; (b) 94°; (c) 103°