The figure is not drawn to scale. PQST is a parallelogram. ∠TPO is 54° and ∠SQR is 26°. PQR is an isosceles triangle and PQ = QR.
- Find ∠ORQ.
- Find ∠PTS.
(a)
∠QOP = 54° (Alternate angles, PT//QS)
∠QOR
= 180° - 54°
= 126° (Angles on a straight line)
∠ORQ
= 180° - 126° - 26°
= 28° (Angles sum of triangle)
(b)
∠QPO = 28° (Isosceles triangle PQR)
∠PTS
= 180° - 54° - 28°
= 98° (Interior angles, PQ//TS)
Answer(s): (a) 28°; (b) 98°