PSLE In the figure, MNST is a parallelogram and PQRS is a rhombus. TSR is a straight line. ∠NMT = 56°, ∠SNP = 29° and ∠QPR = 33°.
- Find ∠NSP.
- Find ∠NPQ.
(a)
∠NST
= ∠NMT
= 56° (Parallelogram)
∠QRP
= ∠QPR
= 33° (Isosceles triangle)
∠PQR
= 180° - 33° - 33°
= 108° (Angles sum of triangle)
∠PSR
= ∠PQR
= 108° (Rhombus)
∠NSP
= 180° - 56° - 108°
= 16° (Angles on a straight line)
(b)
∠NPS
= 180° - 29° - 16°
= 135° (Angles sum of triangle)
∠RPS
= ∠QPR
= 33° (Rhombus)
∠NPQ
= 360° - 135° - 33° - 33°
= 159° (Angles at a point)
Answer(s): (a) 16°; (b) 159°