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° - 138°) ÷ 2
= 42° ÷ 2
= 21° (Isosceles triangle)
∠LNP
= 60° - 21°
= 39° (Equilateral triangle)
(b)
∠LQP
= 60° - 21°
= 39° (Equilateral triangle)
∠LPQ
= 180° - 39° - 21°
= 120° (Angles sum of triangle)
∠LPN
= 360° - 138° - 120°
= 102° (Angles at a point)
∠MLN
= ∠LNP
= 39° (Alternate angles)
∠MLQ
= 60° + 39°
= 99°
Answer(s): (a) 39°; (b) 102°; (c) 99°