PSLE In the figure, NPTU is a parallelogram and QRST is a rhombus. UTS is a straight line. ∠PNU = 60°, ∠TPQ = 26° and ∠RQS = 32°.
- Find ∠PTQ.
- Find ∠PQR.
(a)
∠PTU
= ∠PNU
= 60° (Parallelogram)
∠RSQ
= ∠RQS
= 32° (Isosceles triangle)
∠QRS
= 180° - 32° - 32°
= 102° (Angles sum of triangle)
∠QTS
= ∠QRS
= 102° (Rhombus)
∠PTQ
= 180° - 60° - 102°
= 18° (Angles on a straight line)
(b)
∠PQT
= 180° - 26° - 18°
= 136° (Angles sum of triangle)
∠SQT
= ∠RQS
= 32° (Rhombus)
∠PQR
= 360° - 136° - 32° - 32°
= 160° (Angles at a point)
Answer(s): (a) 18°; (b) 160°