The figure is not drawn to scale. QTVZ is a parallelogram. SWY and RUX are triangles. ∠SWX = 81° and XRU = 54°. Find
- ∠RSW
- the sum of ∠RXU, ∠SNU and ∠UPW.
(a)
∠RSW
= 180° - 81°
= 99° (Interior angles, QT//ZV)
(b)
∠SNU = ∠RNP (Vertically opposite angles)
∠UPW = ∠XPN (Vertically opposite angles)
RXPN is a quadrilateral.
∠RXU + ∠XPN + ∠RNP + 54° = 360° (Sum of angles in a quadrilateral)
∠RXU + ∠XPN + ∠RNP
= 360° - 54°
= 306°
Answer(s): (a) 99°; (b) 306°