PSLE In the figure, MNQ and SRQ are straight lines and RN is parallel to QP. ∠RSM is a right angle, ∠SMN = 52°, ∠MNP = 116° and ∠QRN = 63°.
- Find ∠MNR.
- Find ∠NPQ.
(a)
∠MQS
= 180° - 90° - 52°
= 38° (Angles sum of triangle)
∠QNR
= 180° - 63° - 38°
= 79° (Angles sum of triangle)
∠MNR
= 180° - 79°
= 116° (Angles on a straight line)
(b)
∠QNP
= 360° - 116° - 79° - 116°
= 49° (Angles at a point)
∠NPQ
= 180° - 49° - 49°
= 82°
Answer(s): (a) 116°; (b) 82°