In the figure, PQRS is a trapezium and PSTW is a rhombus. PS is parallel to QR and ST = SU. WSR and SVU are straight lines. ∠SPW = 48° and ∠VSW = 31°. Find
- ∠PSR
- ∠SUT
(a)
∠PSW
= (180° - 48°) ÷ 2
= 66° (Isosceles triangle)
∠PSR
= 180° - 66°
= 114° (Angles on a straight line)
(b)
∠UST
= 66° - 31°
= 35°
∠SUT
= (180° - 35°) ÷ 2
= 72.5 ° (Isosceles triangle)
Answer(s): (a) 114°; (b) 72.5°