The figure is not drawn to scale. NRTX is a parallelogram. QUW and PSV are triangles. ∠QUV = 82° and VPS = 52°. Find
- ∠PQU
- the sum of ∠PVS, ∠QLS and ∠SMU.
(a)
∠PQU
= 180° - 82°
= 98° (Interior angles, NR//XT)
(b)
∠QLS = ∠PLM (Vertically opposite angles)
∠SMU = ∠VML (Vertically opposite angles)
PVML is a quadrilateral.
∠PVS + ∠VML + ∠PLM + 52° = 360° (Sum of angles in a quadrilateral)
∠PVS + ∠VML + ∠PLM
= 360° - 52°
= 308°
Answer(s): (a) 98°; (b) 308°