The figure is not drawn to scale. PQST is a parallelogram. ∠TPO is 60° and ∠SQR is 26°. 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° - 26°
= 34° (Angles sum of triangle)
(b)
∠QPO = 34° (Isosceles triangle PQR)
∠PTS
= 180° - 60° - 34°
= 86° (Interior angles, PQ//TS)
Answer(s): (a) 34°; (b) 86°