PSLE In the figure, LMRS is a parallelogram and NPQR is a rhombus. SRQ is a straight line. ∠MLS = 62°, ∠RMN = 28° and ∠PNQ = 32°.
- Find ∠MRN.
- Find ∠MNP.
(a)
∠MRS
= ∠MLS
= 62° (Parallelogram)
∠PQN
= ∠PNQ
= 32° (Isosceles triangle)
∠NPQ
= 180° - 32° - 32°
= 103° (Angles sum of triangle)
∠NRQ
= ∠NPQ
= 103° (Rhombus)
∠MRN
= 180° - 62° - 103°
= 15° (Angles on a straight line)
(b)
∠MNR
= 180° - 28° - 15°
= 137° (Angles sum of triangle)
∠QNR
= ∠PNQ
= 32° (Rhombus)
∠MNP
= 360° - 137° - 32° - 32°
= 159° (Angles at a point)
Answer(s): (a) 15°; (b) 159°