The figure is not drawn to scale. PQST is a parallelogram. ∠TPO is 57° and ∠SQR is 26°. PQR is an isosceles triangle and PQ = QR.
- Find ∠ORQ.
- Find ∠PTS.
(a)
∠QOP = 57° (Alternate angles, PT//QS)
∠QOR
= 180° - 57°
= 123° (Angles on a straight line)
∠ORQ
= 180° - 123° - 26°
= 31° (Angles sum of triangle)
(b)
∠QPO = 31° (Isosceles triangle PQR)
∠PTS
= 180° - 57° - 31°
= 92° (Interior angles, PQ//TS)
Answer(s): (a) 31°; (b) 92°