The figure is not drawn to scale. LPRV is a parallelogram. NSU and MQT are triangles. ∠NST = 82° and TMQ = 51°. Find
- ∠MNS
- the sum of ∠MTQ, ∠NJQ and ∠QKS.
(a)
∠MNS
= 180° - 82°
= 98° (Interior angles, LP//VR)
(b)
∠NJQ = ∠MJK (Vertically opposite angles)
∠QKS = ∠TKJ (Vertically opposite angles)
MTKJ is a quadrilateral.
∠MTQ + ∠TKJ + ∠MJK + 51° = 360° (Sum of angles in a quadrilateral)
∠MTQ + ∠TKJ + ∠MJK
= 360° - 51°
= 309°
Answer(s): (a) 98°; (b) 309°