The figure is not drawn to scale. TWYC is a parallelogram. VZB and UXA are triangles. ∠VZA = 76° and AUX = 55°. Find
- ∠UVZ
- the sum of ∠UAX, ∠VRX and ∠XSZ.
(a)
∠UVZ
= 180° - 76°
= 104° (Interior angles, TW//CY)
(b)
∠VRX = ∠URS (Vertically opposite angles)
∠XSZ = ∠ASR (Vertically opposite angles)
UASR is a quadrilateral.
∠UAX + ∠ASR + ∠URS + 55° = 360° (Sum of angles in a quadrilateral)
∠UAX + ∠ASR + ∠URS
= 360° - 55°
= 305°
Answer(s): (a) 104°; (b) 305°