The figure is not drawn to scale. Triangle PQN is an isosceles triangle. Triangle LMN is an equilateral triangle. ∠QNP is
15 of ∠MLN and ∠MNQ = ∠LNP.
- Find ∠MNQ.
- Find ∠LPN.
(a)
∠MNL = 60° (Equilateral triangle)
∠QNP
= ∠MNL x
15 = 60° x
15 = 12°
∠MNQ = ∠LNP
∠MNQ
= ∠MNL - ∠QNA) ÷ 2
= (60° - 12°) ÷ 2
= 48° ÷ 2
= 24° (Isosceles triangle)
(b)
∠LPN
= 180° - ∠MLN - ∠MNQ
= 180° - 60° - 24°
= 96° (Angles sum of triangle)
Answer(s): (a) 24°; (b) 96°