In the figure, TWZC is a rectangle, ZACD is a rhombus and WXYZ is a parallelogram. ∠ZAC = 74° and ∠YZA = 97°.
- Find ∠VZW
- Find ∠ZYX
(a)
∠CDZ = ∠CAZ = 74°
∠DZC
= (180° - 74°) ÷ 2
= 106° ÷ 2
= 53° (Isosceles triangle)
∠VZW
= 90° - 53°
= 37°
(b)
∠WZY
= 360° - 97° - 90° - 53°
= 120° (Angles at a point)
∠XYZ
= 180° - 120°
= 60° (Interior Angles, WZ//XF)
Answer(s): (a) 37°; (b) 60°