The figure is not drawn to scale. Triangle NPM is an isosceles triangle. Triangle KLM is an equilateral triangle. ∠PMN is
35 of ∠LKM and ∠LMP = ∠KMN.
- Find ∠LMP.
- Find ∠KNM.
(a)
∠LMK = 60° (Equilateral triangle)
∠PMN
= ∠LMK x
35 = 60° x
35 = 36°
∠LMP = ∠KMN
∠LMP
= ∠LMK - ∠PMA) ÷ 2
= (60° - 36°) ÷ 2
= 24° ÷ 2
= 12° (Isosceles triangle)
(b)
∠KNM
= 180° - ∠LKM - ∠LMP
= 180° - 60° - 12°
= 108° (Angles sum of triangle)
Answer(s): (a) 12°; (b) 108°