In the figure, MQTW is a rectangle, TUWX is a rhombus and QRST is a parallelogram. ∠TUW = 78° and ∠STU = 95°.
- Find ∠PTQ
- Find ∠TSR
(a)
∠WXT = ∠WUT = 78°
∠XTW
= (180° - 78°) ÷ 2
= 102° ÷ 2
= 51° (Isosceles triangle)
∠PTQ
= 90° - 51°
= 39°
(b)
∠QTS
= 360° - 95° - 90° - 51°
= 124° (Angles at a point)
∠RST
= 180° - 124°
= 56° (Interior Angles, QT//RF)
Answer(s): (a) 39°; (b) 56°