In the figure, not drawn to scale, YABC and XZCD are rhombuses. Given that ∠BAZ = 115° and ∠YXD = 126°, find
- ∠XDZ
- ∠ZWY.
(a)
∠XDZ
= (180° - 126°) ÷ 2
= 54 ÷ 2
= 27° (Isosceles triangle, XD = XR)
(b)
∠ZYC
= 180° - 115°
= 65° (Interior angles, BA//CQ)
∠DZX = ∠XDZ = 27° (Isosceles Briangle, XD = XR)
∠ZWY
= 180° - 65° - 27°
= 88° (Angles sum of triangle, WZQ)
Answer(s): (a) 27°; (b) 88°