In the figure, MQTW is a rectangle, TUWX is a rhombus and QRST is a parallelogram. ∠TUW = 76° and ∠STU = 92°.
- Find ∠PTQ
- Find ∠TSR
(a)
∠WXT = ∠WUT = 76°
∠XTW
= (180° - 76°) ÷ 2
= 104° ÷ 2
= 52° (Isosceles triangle)
∠PTQ
= 90° - 52°
= 38°
(b)
∠QTS
= 360° - 92° - 90° - 52°
= 126° (Angles at a point)
∠RST
= 180° - 126°
= 54° (Interior Angles, QT//RF)
Answer(s): (a) 38°; (b) 54°