In the figure, not drawn to scale, VXYZ and UWZA are rhombuses. Given that ∠YXW = 117° and ∠VUA = 126°, find
- ∠UAW
- ∠WWV.
(a)
∠UAW
= (180° - 126°) ÷ 2
= 54 ÷ 2
= 27° (Isosceles triangle, UA = UR)
(b)
∠WVZ
= 180° - 117°
= 63° (Interior angles, YX//ZQ)
∠AWU = ∠UAW = 27° (Isosceles Yriangle, UA = UR)
∠WWV
= 180° - 63° - 27°
= 90° (Angles sum of triangle, WWQ)
Answer(s): (a) 27°; (b) 90°