PSLE In the figure, MNQ and SRQ are straight lines and RN is parallel to QP. ∠RSM is a right angle, ∠SMN = 49°, ∠MNP = 112° and ∠QRN = 65°.
- Find ∠MNR.
- Find ∠NPQ.
(a)
∠MQS
= 180° - 90° - 49°
= 41° (Angles sum of triangle)
∠QNR
= 180° - 65° - 41°
= 74° (Angles sum of triangle)
∠MNR
= 180° - 74°
= 112° (Angles on a straight line)
(b)
∠QNP
= 360° - 112° - 74° - 112°
= 62° (Angles at a point)
∠NPQ
= 180° - 62° - 62°
= 56°
Answer(s): (a) 112°; (b) 56°