PSLE In the figure, LMRS is a parallelogram and NPQR is a rhombus. SRQ is a straight line. ∠MLS = 56°, ∠RMN = 27° and ∠PNQ = 32°.
- Find ∠MRN.
- Find ∠MNP.
(a)
∠MRS
= ∠MLS
= 56° (Parallelogram)
∠PQN
= ∠PNQ
= 32° (Isosceles triangle)
∠NPQ
= 180° - 32° - 32°
= 103° (Angles sum of triangle)
∠NRQ
= ∠NPQ
= 103° (Rhombus)
∠MRN
= 180° - 56° - 103°
= 21° (Angles on a straight line)
(b)
∠MNR
= 180° - 27° - 21°
= 132° (Angles sum of triangle)
∠QNR
= ∠PNQ
= 32° (Rhombus)
∠MNP
= 360° - 132° - 32° - 32°
= 164° (Angles at a point)
Answer(s): (a) 21°; (b) 164°