The figure is not drawn to scale. XYAB is a parallelogram. ∠BXO is 60° and ∠AYZ is 25°. XYZ is an isosceles triangle and XY = YZ.
- Find ∠OZY.
- Find ∠XBA.
(a)
∠YOX = 60° (Alternate angles, XB//YA)
∠YOZ
= 180° - 60°
= 120° (Angles on a straight line)
∠OZY
= 180° - 120° - 25°
= 35° (Angles sum of triangle)
(b)
∠YXO = 35° (Isosceles triangle XYZ)
∠XBA
= 180° - 60° - 35°
= 85° (Interior angles, XY//BA)
Answer(s): (a) 35°; (b) 85°