The figure is not drawn to scale. PSUY is a parallelogram. RVX and QTW are triangles. ∠RVW = 75° and WQT = 51°. Find
- ∠QRV
- the sum of ∠QWT, ∠RMT and ∠TNV.
(a)
∠QRV
= 180° - 75°
= 105° (Interior angles, PS//YU)
(b)
∠RMT = ∠QMN (Vertically opposite angles)
∠TNV = ∠WNM (Vertically opposite angles)
QWNM is a quadrilateral.
∠QWT + ∠WNM + ∠QMN + 51° = 360° (Sum of angles in a quadrilateral)
∠QWT + ∠WNM + ∠QMN
= 360° - 51°
= 309°
Answer(s): (a) 105°; (b) 309°