In the figure, QRST is a trapezium and QTUX is a rhombus. QT is parallel to RS and TU = TV. XTS and TWV are straight lines. ∠TQX = 48° and ∠WTX = 25°. Find
- ∠QTS
- ∠TVU
(a)
∠QTX
= (180° - 48°) ÷ 2
= 66° (Isosceles triangle)
∠QTS
= 180° - 66°
= 114° (Angles on a straight line)
(b)
∠VTU
= 66° - 25°
= 41°
∠TVU
= (180° - 41°) ÷ 2
= 69.5 ° (Isosceles triangle)
Answer(s): (a) 114°; (b) 69.5°