The figure is not drawn to scale. PQST is a parallelogram. ∠TPO is 59° and ∠SQR is 27°. PQR is an isosceles triangle and PQ = QR.
- Find ∠ORQ.
- Find ∠PTS.
(a)
∠QOP = 59° (Alternate angles, PT//QS)
∠QOR
= 180° - 59°
= 121° (Angles on a straight line)
∠ORQ
= 180° - 121° - 27°
= 32° (Angles sum of triangle)
(b)
∠QPO = 32° (Isosceles triangle PQR)
∠PTS
= 180° - 59° - 32°
= 89° (Interior angles, PQ//TS)
Answer(s): (a) 32°; (b) 89°