PSLE In the figure, LMRS is a parallelogram and NPQR is a rhombus. SRQ is a straight line. ∠MLS = 58°, ∠RMN = 29° and ∠PNQ = 32°.
- Find ∠MRN.
- Find ∠MNP.
(a)
∠MRS
= ∠MLS
= 58° (Parallelogram)
∠PQN
= ∠PNQ
= 32° (Isosceles triangle)
∠NPQ
= 180° - 32° - 32°
= 102° (Angles sum of triangle)
∠NRQ
= ∠NPQ
= 102° (Rhombus)
∠MRN
= 180° - 58° - 102°
= 20° (Angles on a straight line)
(b)
∠MNR
= 180° - 29° - 20°
= 131° (Angles sum of triangle)
∠QNR
= ∠PNQ
= 32° (Rhombus)
∠MNP
= 360° - 131° - 32° - 32°
= 165° (Angles at a point)
Answer(s): (a) 20°; (b) 165°