In the figure, not drawn to scale, YABC and XZCD are rhombuses. Given that ∠BAZ = 120° and ∠YXD = 122°, find
- ∠XDZ
- ∠ZWY.
(a)
∠XDZ
= (180° - 122°) ÷ 2
= 58 ÷ 2
= 29° (Isosceles triangle, XD = XR)
(b)
∠ZYC
= 180° - 120°
= 60° (Interior angles, BA//CQ)
∠DZX = ∠XDZ = 29° (Isosceles Briangle, XD = XR)
∠ZWY
= 180° - 60° - 29°
= 91° (Angles sum of triangle, WZQ)
Answer(s): (a) 29°; (b) 91°