The figure is not drawn to scale. KMNP is a trapezium and KM // PN. Given that KP = KL, ∠PKL = 74° and ∠KMN = 100°.
- Find ∠MNP
- Find ∠KLP
- Find ∠LPN
(a)
∠MNP
= 180° - 100°
= 80° (Interior angles, KM//PN)
(b)
∠KLP
= (180° - 74°) ÷ 2
= 106° ÷ 2
= 53° (Isosceles triangle)
(c)
∠LPN
= ∠KLP
= 53° (Alternate angles, KM//PN)
Answer(s): (a) 80°; (b) 53°; (c) 53°