The figure is not drawn to scale. XYAB is a parallelogram. ∠BXO is 54° and ∠AYZ is 29°. XYZ is an isosceles triangle and XY = YZ.
- Find ∠OZY.
- Find ∠XBA.
(a)
∠YOX = 54° (Alternate angles, XB//YA)
∠YOZ
= 180° - 54°
= 126° (Angles on a straight line)
∠OZY
= 180° - 126° - 29°
= 25° (Angles sum of triangle)
(b)
∠YXO = 25° (Isosceles triangle XYZ)
∠XBA
= 180° - 54° - 25°
= 101° (Interior angles, XY//BA)
Answer(s): (a) 25°; (b) 101°