In the figure, MNR and QNP are right-angled triangles. RN is parallel to QP. Find
- ∠NPQ
- ∠NRQ
(a)
∠QNR
= 360° - 90° - 90° - 123°
= 57° (Angles at a point)
∠NQP = ∠QNR = 57° (Alternate angles)
∠NPQ
= 180° - ∠QNP - ∠NQP
= 180° - 90° - 57°
= 33° (Angles sum of triangle)
(b)
∠NRQ
= 180° - ∠QNR - ∠NQR
= 180° - 57° - 80°
= 43° (Angles sum of triangle)
Answer(s): (a) 33°; (b) 43°