PSLE In the figure, MNQ and SRQ are straight lines and RN is parallel to QP. ∠RSM is a right angle, ∠SMN = 55°, ∠MNP = 111° and ∠QRN = 68°.
- Find ∠MNR.
- Find ∠NPQ.
(a)
∠MQS
= 180° - 90° - 55°
= 35° (Angles sum of triangle)
∠QNR
= 180° - 68° - 35°
= 77° (Angles sum of triangle)
∠MNR
= 180° - 77°
= 111° (Angles on a straight line)
(b)
∠QNP
= 360° - 111° - 77° - 111°
= 61° (Angles at a point)
∠NPQ
= 180° - 61° - 61°
= 58°
Answer(s): (a) 111°; (b) 58°