The figure is not drawn to scale. Triangle STR is an isosceles triangle. Triangle PQR is an equilateral triangle. ∠TRS is
15 of ∠QPR and ∠QRT = ∠PRS.
- Find ∠QRT.
- Find ∠PSR.
(a)
∠QRP = 60° (Equilateral triangle)
∠TRS
= ∠QRP x
15 = 60° x
15 = 12°
∠QRT = ∠PRS
∠QRT
= ∠QRP - ∠TRA) ÷ 2
= (60° - 12°) ÷ 2
= 48° ÷ 2
= 24° (Isosceles triangle)
(b)
∠PSR
= 180° - ∠QPR - ∠QRT
= 180° - 60° - 24°
= 96° (Angles sum of triangle)
Answer(s): (a) 24°; (b) 96°