PSLE In the figure, NPQR is a parallelogram. LRN and MRQ are straight lines and LM = MN. ∠LMR = 28° and ∠PQR = 57°.
- Find ∠QRN.
- Find ∠RMN.
(a)
∠QRN
= 180° - 57°
= 123° (Interior angles)
(b)
∠LRM
= ∠QRN
= 123° (Vertically opposite angles)
∠MLR
= 180° - 123° - 28°
= 29° (Angles sum of triangle)
∠MNR = ∠MLR (Isosceles triangle)
∠LMN
= 180° - 29° - 29°
= 122° (Angles sum of triangle)
∠RMN
= 122° - 28°
= 94°
Answer(s): (a) 123°; (b) 94°