The figure is not drawn to scale. XACG is a parallelogram. ZDF and YBE are triangles. ∠ZDE = 75° and EYB = 51°. Find
- ∠YZD
- the sum of ∠YEB, ∠ZVB and ∠BWD.
(a)
∠YZD
= 180° - 75°
= 105° (Interior angles, XA//GC)
(b)
∠ZVB = ∠YVW (Vertically opposite angles)
∠BWD = ∠EWV (Vertically opposite angles)
YEWV is a quadrilateral.
∠YEB + ∠EWV + ∠YVW + 51° = 360° (Sum of angles in a quadrilateral)
∠YEB + ∠EWV + ∠YVW
= 360° - 51°
= 309°
Answer(s): (a) 105°; (b) 309°