PSLEKLMN is a parallelogram, KMP is an equilateral triangle and MN = NP.
- Find ∠KMN.
- Find ∠MNK.
- Find ∠PKL.
(a)
MN = NP
Triangle MNP is an isosceles triangle.
∠NMP
= (180° - 142°) ÷ 2
= 38° ÷ 2
= 19° (Isosceles triangle)
∠KMN
= 60° - 19°
= 41° (Equilateral triangle)
(b)
∠KPN
= 60° - 19°
= 41° (Equilateral triangle)
∠KNP
= 180° - 41° - 19°
= 120° (Angles sum of triangle)
∠KNM
= 360° - 142° - 120°
= 98° (Angles at a point)
∠LKM
= ∠KMN
= 41° (Alternate angles)
∠LKP
= 60° + 41°
= 101°
Answer(s): (a) 41°; (b) 98°; (c) 101°