In the figure, LMNP is a quadrilateral where ∠LMN = 128° and ∠MNP = 114°. ∠NPQ = 80° and MN = NP. The point Q on LP is such that MQ is parallel to NP. Calculate
- ∠MPQ
- ∠MLQ
(a)
∠NPM
= (180° - 114°) ÷ 2
= 33° (Isosceles triangle)
∠MPQ
= 80° - 33°
= 47°
(b)
∠MLQ
= 360° - 114° - 80° - 128°
= 38° (Sum of angles in a quadrilateral)
Answer(s): (a) 47°; (b) 38°