The figure is not drawn to scale. PRST is a trapezium and PR // TS. Given that PT = PQ, ∠TPQ = 74° and ∠PRS = 99°.
- Find ∠RST
- Find ∠PQT
- Find ∠QTS
(a)
∠RST
= 180° - 99°
= 81° (Interior angles, PR//TS)
(b)
∠PQT
= (180° - 74°) ÷ 2
= 106° ÷ 2
= 53° (Isosceles triangle)
(c)
∠QTS
= ∠PQT
= 53° (Alternate angles, PR//TS)
Answer(s): (a) 81°; (b) 53°; (c) 53°