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° - 132°) ÷ 2
= 48° ÷ 2
= 24° (Isosceles triangle)
∠LNP
= 60° - 24°
= 36° (Equilateral triangle)
(b)
∠LQP
= 60° - 24°
= 36° (Equilateral triangle)
∠LPQ
= 180° - 36° - 24°
= 120° (Angles sum of triangle)
∠LPN
= 360° - 132° - 120°
= 108° (Angles at a point)
∠MLN
= ∠LNP
= 36° (Alternate angles)
∠MLQ
= 60° + 36°
= 96°
Answer(s): (a) 36°; (b) 108°; (c) 96°