In the figure, TWZC is a rectangle, ZACD is a rhombus and WXYZ is a parallelogram. ∠ZAC = 72° and ∠YZA = 96°.
- Find ∠VZW
- Find ∠ZYX
(a)
∠CDZ = ∠CAZ = 72°
∠DZC
= (180° - 72°) ÷ 2
= 108° ÷ 2
= 54° (Isosceles triangle)
∠VZW
= 90° - 54°
= 36°
(b)
∠WZY
= 360° - 96° - 90° - 54°
= 120° (Angles at a point)
∠XYZ
= 180° - 120°
= 60° (Interior Angles, WZ//XF)
Answer(s): (a) 36°; (b) 60°