The figure is not drawn to scale. WZBF is a parallelogram. YCE and XAD are triangles. ∠YCD = 78° and DXA = 54°. Find
- ∠XYC
- the sum of ∠XDA, ∠YUA and ∠AVC.
(a)
∠XYC
= 180° - 78°
= 102° (Interior angles, WZ//FB)
(b)
∠YUA = ∠XUV (Vertically opposite angles)
∠AVC = ∠DVU (Vertically opposite angles)
XDVU is a quadrilateral.
∠XDA + ∠DVU + ∠XUV + 54° = 360° (Sum of angles in a quadrilateral)
∠XDA + ∠DVU + ∠XUV
= 360° - 54°
= 306°
Answer(s): (a) 102°; (b) 306°