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 = 42° and ∠VSW = 30°. Find
- ∠PSR
- ∠SUT
(a)
∠PSW
= (180° - 42°) ÷ 2
= 69° (Isosceles triangle)
∠PSR
= 180° - 69°
= 111° (Angles on a straight line)
(b)
∠UST
= 69° - 30°
= 39°
∠SUT
= (180° - 39°) ÷ 2
= 70.5 ° (Isosceles triangle)
Answer(s): (a) 111°; (b) 70.5°