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° - 134°) ÷ 2
= 46° ÷ 2
= 23° (Isosceles triangle)
∠KMN
= 60° - 23°
= 37° (Equilateral triangle)
(b)
∠KPN
= 60° - 23°
= 37° (Equilateral triangle)
∠KNP
= 180° - 37° - 23°
= 120° (Angles sum of triangle)
∠KNM
= 360° - 134° - 120°
= 106° (Angles at a point)
∠LKM
= ∠KMN
= 37° (Alternate angles)
∠LKP
= 60° + 37°
= 97°
Answer(s): (a) 37°; (b) 106°; (c) 97°
