The figure is not drawn to scale. WZBF is a parallelogram. YCE and XAD are triangles. ∠YCD = 77° and DXA = 56°. Find
- ∠XYC
- the sum of ∠XDA, ∠YUA and ∠AVC.
(a)
∠XYC
= 180° - 77°
= 103° (Interior angles, WZ//FB)
(b)
∠YUA = ∠XUV (Vertically opposite angles)
∠AVC = ∠DVU (Vertically opposite angles)
XDVU is a quadrilateral.
∠XDA + ∠DVU + ∠XUV + 56° = 360° (Sum of angles in a quadrilateral)
∠XDA + ∠DVU + ∠XUV
= 360° - 56°
= 304°
Answer(s): (a) 103°; (b) 304°