In the figure, VYBE is a rectangle, BCEF is a rhombus and YZAB is a parallelogram. ∠BCE = 78° and ∠ABC = 97°.
- Find ∠XBY
- Find ∠BAZ
(a)
∠EFB = ∠ECB = 78°
∠FBE
= (180° - 78°) ÷ 2
= 102° ÷ 2
= 51° (Isosceles triangle)
∠XBY
= 90° - 51°
= 39°
(b)
∠YBA
= 360° - 97° - 90° - 51°
= 122° (Angles at a point)
∠ZAB
= 180° - 122°
= 58° (Interior Angles, YB//ZF)
Answer(s): (a) 39°; (b) 58°