In the figure, MQTW is a rectangle, TUWX is a rhombus and QRST is a parallelogram. ∠TUW = 80° and ∠STU = 97°.
- Find ∠PTQ
- Find ∠TSR
(a)
∠WXT = ∠WUT = 80°
∠XTW
= (180° - 80°) ÷ 2
= 100° ÷ 2
= 50° (Isosceles triangle)
∠PTQ
= 90° - 50°
= 40°
(b)
∠QTS
= 360° - 97° - 90° - 50°
= 123° (Angles at a point)
∠RST
= 180° - 123°
= 57° (Interior Angles, QT//RF)
Answer(s): (a) 40°; (b) 57°