PSLE In the figure, QRST is a parallelogram. NTQ and PTS are straight lines and NP = PQ. ∠NPT = 30° and ∠RST = 58°.
- Find ∠STQ.
- Find ∠TPQ.
(a)
∠STQ
= 180° - 58°
= 122° (Interior angles)
(b)
∠NTP
= ∠STQ
= 122° (Vertically opposite angles)
∠PNT
= 180° - 122° - 30°
= 28° (Angles sum of triangle)
∠PQT = ∠PNT (Isosceles triangle)
∠NPQ
= 180° - 28° - 28°
= 124° (Angles sum of triangle)
∠TPQ
= 124° - 30°
= 94°
Answer(s): (a) 122°; (b) 94°