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° - 150°) ÷ 2
= 30° ÷ 2
= 15° (Isosceles triangle)
∠KMN
= 60° - 15°
= 45° (Equilateral triangle)
(b)
∠KPN
= 60° - 15°
= 45° (Equilateral triangle)
∠KNP
= 180° - 45° - 15°
= 120° (Angles sum of triangle)
∠KNM
= 360° - 150° - 120°
= 90° (Angles at a point)
∠LKM
= ∠KMN
= 45° (Alternate angles)
∠LKP
= 60° + 45°
= 105°
Answer(s): (a) 45°; (b) 90°; (c) 105°