In the figure, not drawn to scale, VWXY is a square, XYZ is an equilateral triangle, XZAB is a rhombus, and WX = ZX. Find
- ∠ZAB
- ∠VZW
(a)
∠YXZ = 60°
∠WXZ
= 90° - 60°
= 30°
XZ = XW
∠XZW
= (180° - 30°) ÷ 2
= 150° ÷ 2
= 75° (Isosceles triangle)
∠ZAB
= 180° - 75°
= 105° (Interior angles)
(b)
∠XWZ = ∠XZW = 75°
∠VWZ
= 90° - 75°
= 15°
∠VZW
= 180° - 15° - 15°
= 150° (Isosceles triangle)
Answer(s): (a) 105°; (b) 150°