In the figure, UXAD is a rectangle, ABDE is a rhombus and XYZA is a parallelogram. ∠ABD = 78° and ∠ZAB = 91°.
- Find ∠WAX
- Find ∠AZY
(a)
∠DEA = ∠DBA = 78°
∠EAD
= (180° - 78°) ÷ 2
= 102° ÷ 2
= 51° (Isosceles triangle)
∠WAX
= 90° - 51°
= 39°
(b)
∠XAZ
= 360° - 91° - 90° - 51°
= 128° (Angles at a point)
∠YZA
= 180° - 128°
= 52° (Interior Angles, XA//YF)
Answer(s): (a) 39°; (b) 52°