In the figure, LMNP is a quadrilateral where ∠LMN = 136° and ∠MNP = 112°. ∠NPQ = 80° and MN = NP. The point Q on LP is such that MQ is parallel to NP. Calculate
- ∠MPQ
- ∠MLQ
(a)
∠NPM
= (180° - 112°) ÷ 2
= 34° (Isosceles triangle)
∠MPQ
= 80° - 34°
= 46°
(b)
∠MLQ
= 360° - 112° - 80° - 136°
= 32° (Sum of angles in a quadrilateral)
Answer(s): (a) 46°; (b) 32°