In the figure, VYBE is a rectangle, BCEF is a rhombus and YZAB is a parallelogram. ∠BCE = 72° and ∠ABC = 97°.
- Find ∠XBY
- Find ∠BAZ
(a)
∠EFB = ∠ECB = 72°
∠FBE
= (180° - 72°) ÷ 2
= 108° ÷ 2
= 54° (Isosceles triangle)
∠XBY
= 90° - 54°
= 36°
(b)
∠YBA
= 360° - 97° - 90° - 54°
= 119° (Angles at a point)
∠ZAB
= 180° - 119°
= 61° (Interior Angles, YB//ZF)
Answer(s): (a) 36°; (b) 61°