In the figure, TWZC is a rectangle, ZACD is a rhombus and WXYZ is a parallelogram. ∠ZAC = 80° and ∠YZA = 93°.
- Find ∠VZW
- Find ∠ZYX
(a)
∠CDZ = ∠CAZ = 80°
∠DZC
= (180° - 80°) ÷ 2
= 100° ÷ 2
= 50° (Isosceles triangle)
∠VZW
= 90° - 50°
= 40°
(b)
∠WZY
= 360° - 93° - 90° - 50°
= 127° (Angles at a point)
∠XYZ
= 180° - 127°
= 53° (Interior Angles, WZ//XF)
Answer(s): (a) 40°; (b) 53°