The figure is not drawn to scale. Triangle QRP is an isosceles triangle. Triangle MNP is an equilateral triangle. ∠RPQ is
15 of ∠NMP and ∠NPR = ∠MPQ.
- Find ∠NPR.
- Find ∠MQP.
(a)
∠NPM = 60° (Equilateral triangle)
∠RPQ
= ∠NPM x
15 = 60° x
15 = 12°
∠NPR = ∠MPQ
∠NPR
= ∠NPM - ∠RPA) ÷ 2
= (60° - 12°) ÷ 2
= 48° ÷ 2
= 24° (Isosceles triangle)
(b)
∠MQP
= 180° - ∠NMP - ∠NPR
= 180° - 60° - 24°
= 96° (Angles sum of triangle)
Answer(s): (a) 24°; (b) 96°