The figure is not drawn to scale. QTVZ is a parallelogram. SWY and RUX are triangles. ∠SWX = 83° and XRU = 51°. Find
- ∠RSW
- the sum of ∠RXU, ∠SNU and ∠UPW.
(a)
∠RSW
= 180° - 83°
= 97° (Interior angles, QT//ZV)
(b)
∠SNU = ∠RNP (Vertically opposite angles)
∠UPW = ∠XPN (Vertically opposite angles)
RXPN is a quadrilateral.
∠RXU + ∠XPN + ∠RNP + 51° = 360° (Sum of angles in a quadrilateral)
∠RXU + ∠XPN + ∠RNP
= 360° - 51°
= 309°
Answer(s): (a) 97°; (b) 309°