The figure is not drawn to scale. NRTX is a parallelogram. QUW and PSV are triangles. ∠QUV = 80° and VPS = 51°. Find
- ∠PQU
- the sum of ∠PVS, ∠QLS and ∠SMU.
(a)
∠PQU
= 180° - 80°
= 100° (Interior angles, NR//XT)
(b)
∠QLS = ∠PLM (Vertically opposite angles)
∠SMU = ∠VML (Vertically opposite angles)
PVML is a quadrilateral.
∠PVS + ∠VML + ∠PLM + 51° = 360° (Sum of angles in a quadrilateral)
∠PVS + ∠VML + ∠PLM
= 360° - 51°
= 309°
Answer(s): (a) 100°; (b) 309°