PSLE In the figure, NPQR is a parallelogram. LRN and MRQ are straight lines and LM = MN. ∠LMR = 32° and ∠PQR = 58°.
- Find ∠QRN.
- Find ∠RMN.
(a)
∠QRN
= 180° - 58°
= 122° (Interior angles)
(b)
∠LRM
= ∠QRN
= 122° (Vertically opposite angles)
∠MLR
= 180° - 122° - 32°
= 26° (Angles sum of triangle)
∠MNR = ∠MLR (Isosceles triangle)
∠LMN
= 180° - 26° - 26°
= 128° (Angles sum of triangle)
∠RMN
= 128° - 32°
= 96°
Answer(s): (a) 122°; (b) 96°