PSLE In the figure, NPTU is a parallelogram and QRST is a rhombus. UTS is a straight line. ∠PNU = 58°, ∠TPQ = 29° and ∠RQS = 32°.
- Find ∠PTQ.
- Find ∠PQR.
(a)
∠PTU
= ∠PNU
= 58° (Parallelogram)
∠RSQ
= ∠RQS
= 32° (Isosceles triangle)
∠QRS
= 180° - 32° - 32°
= 106° (Angles sum of triangle)
∠QTS
= ∠QRS
= 106° (Rhombus)
∠PTQ
= 180° - 58° - 106°
= 16° (Angles on a straight line)
(b)
∠PQT
= 180° - 29° - 16°
= 135° (Angles sum of triangle)
∠SQT
= ∠RQS
= 32° (Rhombus)
∠PQR
= 360° - 135° - 32° - 32°
= 161° (Angles at a point)
Answer(s): (a) 16°; (b) 161°