PSLE In the figure, QRST is a parallelogram. NTQ and PTS are straight lines and NP = PQ. ∠NPT = 27° and ∠RST = 57°.
- Find ∠STQ.
- Find ∠TPQ.
(a)
∠STQ
= 180° - 57°
= 123° (Interior angles)
(b)
∠NTP
= ∠STQ
= 123° (Vertically opposite angles)
∠PNT
= 180° - 123° - 27°
= 30° (Angles sum of triangle)
∠PQT = ∠PNT (Isosceles triangle)
∠NPQ
= 180° - 30° - 30°
= 120° (Angles sum of triangle)
∠TPQ
= 120° - 27°
= 93°
Answer(s): (a) 123°; (b) 93°