The figure is not drawn to scale. PRST is a trapezium and PR // TS. Given that PT = PQ, ∠TPQ = 75° and ∠PRS = 98°.
- Find ∠RST
- Find ∠PQT
- Find ∠QTS
(a)
∠RST
= 180° - 98°
= 82° (Interior angles, PR//TS)
(b)
∠PQT
= (180° - 75°) ÷ 2
= 105° ÷ 2
= 52.5° (Isosceles triangle)
(c)
∠QTS
= ∠PQT
= 52.5° (Alternate angles, PR//TS)
Answer(s): (a) 82°; (b) 52.5°; (c) 52.5°