The figure is not drawn to scale. PQST is a parallelogram. ∠TPO is 60° and ∠SQR is 28°. PQR is an isosceles triangle and PQ = QR.
- Find ∠ORQ.
- Find ∠PTS.
(a)
∠QOP = 60° (Alternate angles, PT//QS)
∠QOR
= 180° - 60°
= 120° (Angles on a straight line)
∠ORQ
= 180° - 120° - 28°
= 32° (Angles sum of triangle)
(b)
∠QPO = 32° (Isosceles triangle PQR)
∠PTS
= 180° - 60° - 32°
= 88° (Interior angles, PQ//TS)
Answer(s): (a) 32°; (b) 88°