In the figure, TWZC is a rectangle, ZACD is a rhombus and WXYZ is a parallelogram. ∠ZAC = 76° and ∠YZA = 92°.
- Find ∠VZW
- Find ∠ZYX
(a)
∠CDZ = ∠CAZ = 76°
∠DZC
= (180° - 76°) ÷ 2
= 104° ÷ 2
= 52° (Isosceles triangle)
∠VZW
= 90° - 52°
= 38°
(b)
∠WZY
= 360° - 92° - 90° - 52°
= 126° (Angles at a point)
∠XYZ
= 180° - 126°
= 54° (Interior Angles, WZ//XF)
Answer(s): (a) 38°; (b) 54°