The figure is not drawn to scale. PSUY is a parallelogram. RVX and QTW are triangles. ∠RVW = 78° and WQT = 52°. Find
- ∠QRV
- the sum of ∠QWT, ∠RMT and ∠TNV.
(a)
∠QRV
= 180° - 78°
= 102° (Interior angles, PS//YU)
(b)
∠RMT = ∠QMN (Vertically opposite angles)
∠TNV = ∠WNM (Vertically opposite angles)
QWNM is a quadrilateral.
∠QWT + ∠WNM + ∠QMN + 52° = 360° (Sum of angles in a quadrilateral)
∠QWT + ∠WNM + ∠QMN
= 360° - 52°
= 308°
Answer(s): (a) 102°; (b) 308°