PSLE In the figure, MNST is a parallelogram and PQRS is a rhombus. TSR is a straight line. ∠NMT = 57°, ∠SNP = 29° and ∠QPR = 32°.
- Find ∠NSP.
- Find ∠NPQ.
(a)
∠NST
= ∠NMT
= 57° (Parallelogram)
∠QRP
= ∠QPR
= 32° (Isosceles triangle)
∠PQR
= 180° - 32° - 32°
= 103° (Angles sum of triangle)
∠PSR
= ∠PQR
= 103° (Rhombus)
∠NSP
= 180° - 57° - 103°
= 20° (Angles on a straight line)
(b)
∠NPS
= 180° - 29° - 20°
= 131° (Angles sum of triangle)
∠RPS
= ∠QPR
= 32° (Rhombus)
∠NPQ
= 360° - 131° - 32° - 32°
= 165° (Angles at a point)
Answer(s): (a) 20°; (b) 165°