PSLE In the figure, LMRS is a parallelogram and NPQR is a rhombus. SRQ is a straight line. ∠MLS = 59°, ∠RMN = 28° and ∠PNQ = 33°.
- Find ∠MRN.
- Find ∠MNP.
(a)
∠MRS
= ∠MLS
= 59° (Parallelogram)
∠PQN
= ∠PNQ
= 33° (Isosceles triangle)
∠NPQ
= 180° - 33° - 33°
= 104° (Angles sum of triangle)
∠NRQ
= ∠NPQ
= 104° (Rhombus)
∠MRN
= 180° - 59° - 104°
= 17° (Angles on a straight line)
(b)
∠MNR
= 180° - 28° - 17°
= 135° (Angles sum of triangle)
∠QNR
= ∠PNQ
= 33° (Rhombus)
∠MNP
= 360° - 135° - 33° - 33°
= 159° (Angles at a point)
Answer(s): (a) 17°; (b) 159°