In the figure, TWZC is a rectangle, ZACD is a rhombus and WXYZ is a parallelogram. ∠ZAC = 78° and ∠YZA = 97°.
- Find ∠VZW
- Find ∠ZYX
(a)
∠CDZ = ∠CAZ = 78°
∠DZC
= (180° - 78°) ÷ 2
= 102° ÷ 2
= 51° (Isosceles triangle)
∠VZW
= 90° - 51°
= 39°
(b)
∠WZY
= 360° - 97° - 90° - 51°
= 122° (Angles at a point)
∠XYZ
= 180° - 122°
= 58° (Interior Angles, WZ//XF)
Answer(s): (a) 39°; (b) 58°