PSLE In the figure, NPTU is a parallelogram and QRST is a rhombus. UTS is a straight line. ∠PNU = 57°, ∠TPQ = 29° and ∠RQS = 35°.
- Find ∠PTQ.
- Find ∠PQR.
(a)
∠PTU
= ∠PNU
= 57° (Parallelogram)
∠RSQ
= ∠RQS
= 35° (Isosceles triangle)
∠QRS
= 180° - 35° - 35°
= 103° (Angles sum of triangle)
∠QTS
= ∠QRS
= 103° (Rhombus)
∠PTQ
= 180° - 57° - 103°
= 20° (Angles on a straight line)
(b)
∠PQT
= 180° - 29° - 20°
= 131° (Angles sum of triangle)
∠SQT
= ∠RQS
= 35° (Rhombus)
∠PQR
= 360° - 131° - 35° - 35°
= 159° (Angles at a point)
Answer(s): (a) 20°; (b) 159°