In the figure, LMQ and PMN are right-angled triangles. QM is parallel to PN. Find
- ∠MNP
- ∠MQP
(a)
∠PMQ
= 360° - 90° - 90° - 123°
= 57° (Angles at a point)
∠MPN = ∠PMQ = 57° (Alternate angles)
∠MNP
= 180° - ∠PMN - ∠MPN
= 180° - 90° - 57°
= 33° (Angles sum of triangle)
(b)
∠MQP
= 180° - ∠PMQ - ∠MPQ
= 180° - 57° - 87°
= 36° (Angles sum of triangle)
Answer(s): (a) 33°; (b) 36°