PSLE In the figure, NPQR is a parallelogram. LRN and MRQ are straight lines and LM = MN. ∠LMR = 24° and ∠PQR = 56°.
- Find ∠QRN.
- Find ∠RMN.
(a)
∠QRN
= 180° - 56°
= 124° (Interior angles)
(b)
∠LRM
= ∠QRN
= 124° (Vertically opposite angles)
∠MLR
= 180° - 124° - 24°
= 32° (Angles sum of triangle)
∠MNR = ∠MLR (Isosceles triangle)
∠LMN
= 180° - 32° - 32°
= 116° (Angles sum of triangle)
∠RMN
= 116° - 24°
= 92°
Answer(s): (a) 124°; (b) 92°