PSLE In the figure, MNQ and SRQ are straight lines and RN is parallel to QP. ∠RSM is a right angle, ∠SMN = 53°, ∠MNP = 116° and ∠QRN = 71°.
- Find ∠MNR.
- Find ∠NPQ.
(a)
∠MQS
= 180° - 90° - 53°
= 37° (Angles sum of triangle)
∠QNR
= 180° - 71° - 37°
= 72° (Angles sum of triangle)
∠MNR
= 180° - 72°
= 116° (Angles on a straight line)
(b)
∠QNP
= 360° - 116° - 72° - 116°
= 56° (Angles at a point)
∠NPQ
= 180° - 56° - 56°
= 68°
Answer(s): (a) 116°; (b) 68°