The figure is not drawn to scale. Triangle QRP is an isosceles triangle. Triangle MNP is an equilateral triangle. ∠RPQ is
25 of ∠NMP and ∠NPR = ∠MPQ.
- Find ∠NPR.
- Find ∠MQP.
(a)
∠NPM = 60° (Equilateral triangle)
∠RPQ
= ∠NPM x
25 = 60° x
25 = 24°
∠NPR = ∠MPQ
∠NPR
= ∠NPM - ∠RPA) ÷ 2
= (60° - 24°) ÷ 2
= 36° ÷ 2
= 18° (Isosceles triangle)
(b)
∠MQP
= 180° - ∠NMP - ∠NPR
= 180° - 60° - 18°
= 102° (Angles sum of triangle)
Answer(s): (a) 18°; (b) 102°