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° - 148°) ÷ 2
= 32° ÷ 2
= 16° (Isosceles triangle)
∠KMN
= 60° - 16°
= 44° (Equilateral triangle)
(b)
∠KPN
= 60° - 16°
= 44° (Equilateral triangle)
∠KNP
= 180° - 44° - 16°
= 120° (Angles sum of triangle)
∠KNM
= 360° - 148° - 120°
= 92° (Angles at a point)
∠LKM
= ∠KMN
= 44° (Alternate angles)
∠LKP
= 60° + 44°
= 104°
Answer(s): (a) 44°; (b) 92°; (c) 104°