QRST is a quadrilateral and OQTS is a trapezium in which OQ // TS and ∠RQT = 113°, ∠QTS = 126°, ∠RST = 65° and TS = TQ. Find
- ∠QRO
- ∠TQO
- ∠QST.
(a)
∠QRO
= 360° - 126° -113° - 65°
= 56° (Sum of angles in a quadrilateral)
(b)
∠TQO
= 180° - 126°
= 54° (Interior angles, QO//TC)
(c)
∠QST
= (180° - 126°) ÷ 2
= 54 ÷ 2
= 27° (Isosceles triangle)
Answer(s): (a) 56°; (b) 54°; (c) 27°