In the figure, UXAD is a rectangle, ABDE is a rhombus and XYZA is a parallelogram. ∠ABD = 72° and ∠ZAB = 96°.
- Find ∠WAX
- Find ∠AZY
(a)
∠DEA = ∠DBA = 72°
∠EAD
= (180° - 72°) ÷ 2
= 108° ÷ 2
= 54° (Isosceles triangle)
∠WAX
= 90° - 54°
= 36°
(b)
∠XAZ
= 360° - 96° - 90° - 54°
= 120° (Angles at a point)
∠YZA
= 180° - 120°
= 60° (Interior Angles, XA//YF)
Answer(s): (a) 36°; (b) 60°