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 = 52° and ∠VSW = 30°. Find
- ∠PSR
- ∠SUT
(a)
∠PSW
= (180° - 52°) ÷ 2
= 64° (Isosceles triangle)
∠PSR
= 180° - 64°
= 116° (Angles on a straight line)
(b)
∠UST
= 64° - 30°
= 34°
∠SUT
= (180° - 34°) ÷ 2
= 73 ° (Isosceles triangle)
Answer(s): (a) 116°; (b) 73°