PSLE In the figure, LMP and RQP are straight lines and QM is parallel to PN. ∠QRL is a right angle, ∠RLM = 54°, ∠LMN = 114° and ∠PQM = 67°.
- Find ∠LMQ.
- Find ∠MNP.
(a)
∠LPR
= 180° - 90° - 54°
= 36° (Angles sum of triangle)
∠PMQ
= 180° - 67° - 36°
= 77° (Angles sum of triangle)
∠LMQ
= 180° - 77°
= 114° (Angles on a straight line)
(b)
∠PMN
= 360° - 114° - 77° - 114°
= 55° (Angles at a point)
∠MNP
= 180° - 55° - 55°
= 70°
Answer(s): (a) 114°; (b) 70°