PSLE In the figure, NPTU is a parallelogram and QRST is a rhombus. UTS is a straight line. ∠PNU = 56°, ∠TPQ = 29° and ∠RQS = 33°.
- Find ∠PTQ.
- Find ∠PQR.
(a)
∠PTU
= ∠PNU
= 56° (Parallelogram)
∠RSQ
= ∠RQS
= 33° (Isosceles triangle)
∠QRS
= 180° - 33° - 33°
= 102° (Angles sum of triangle)
∠QTS
= ∠QRS
= 102° (Rhombus)
∠PTQ
= 180° - 56° - 102°
= 22° (Angles on a straight line)
(b)
∠PQT
= 180° - 29° - 22°
= 129° (Angles sum of triangle)
∠SQT
= ∠RQS
= 33° (Rhombus)
∠PQR
= 360° - 129° - 33° - 33°
= 165° (Angles at a point)
Answer(s): (a) 22°; (b) 165°