The figure is not drawn to scale. NPS is an equilateral triangle and RPQ is an isosceles triangle. QPN and PRT are straight lines and QN//TS. ∠SPT = 90° and ∠RSP = 54°.
- Find ∠QPT.
- Find ∠PRQ.
- Find ∠SRT.
(a)
∠SPN = 60° (Equilateral triangle NPY)
∠SPT = 90°
∠RSP = 54°
∠QPT
= 180° - ∠SPT - ∠SPN
= 180° - 90° - 60°
= 30° (Angles on a straight line)
(b)
∠PRQ
= (180° - ∠QPT ÷ 2
= (180° - 30°) ÷ 2
= 150° ÷ 2
= 75° (Isosceles triangle)
(c)
∠SRP
= 180° - ∠SPT - ∠RSP
= 180° - 90° - 54°
= 36°
∠SRT
= 180° - ∠SRP
= 180° - 36°
= 144° (Angles on a straight line)
Answer(s): (a) 30°; (b) 75°; (c) 144°
