In the figure, MQTW is a rectangle, TUWX is a rhombus and QRST is a parallelogram. ∠TUW = 72° and ∠STU = 96°.
- Find ∠PTQ
- Find ∠TSR
(a)
∠WXT = ∠WUT = 72°
∠XTW
= (180° - 72°) ÷ 2
= 108° ÷ 2
= 54° (Isosceles triangle)
∠PTQ
= 90° - 54°
= 36°
(b)
∠QTS
= 360° - 96° - 90° - 54°
= 120° (Angles at a point)
∠RST
= 180° - 120°
= 60° (Interior Angles, QT//RF)
Answer(s): (a) 36°; (b) 60°