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° - 144°) ÷ 2
= 36° ÷ 2
= 18° (Isosceles triangle)
∠KMN
= 60° - 18°
= 42° (Equilateral triangle)
(b)
∠KPN
= 60° - 18°
= 42° (Equilateral triangle)
∠KNP
= 180° - 42° - 18°
= 120° (Angles sum of triangle)
∠KNM
= 360° - 144° - 120°
= 96° (Angles at a point)
∠LKM
= ∠KMN
= 42° (Alternate angles)
∠LKP
= 60° + 42°
= 102°
Answer(s): (a) 42°; (b) 96°; (c) 102°