The figure is not drawn to scale. QTVZ is a parallelogram. SWY and RUX are triangles. ∠SWX = 78° and XRU = 53°. Find
- ∠RSW
- the sum of ∠RXU, ∠SNU and ∠UPW.
(a)
∠RSW
= 180° - 78°
= 102° (Interior angles, QT//ZV)
(b)
∠SNU = ∠RNP (Vertically opposite angles)
∠UPW = ∠XPN (Vertically opposite angles)
RXPN is a quadrilateral.
∠RXU + ∠XPN + ∠RNP + 53° = 360° (Sum of angles in a quadrilateral)
∠RXU + ∠XPN + ∠RNP
= 360° - 53°
= 307°
Answer(s): (a) 102°; (b) 307°