The figure is not drawn to scale. XYAB is a parallelogram. ∠BXO is 55° and ∠AYZ is 30°. XYZ is an isosceles triangle and XY = YZ.
- Find ∠OZY.
- Find ∠XBA.
(a)
∠YOX = 55° (Alternate angles, XB//YA)
∠YOZ
= 180° - 55°
= 125° (Angles on a straight line)
∠OZY
= 180° - 125° - 30°
= 25° (Angles sum of triangle)
(b)
∠YXO = 25° (Isosceles triangle XYZ)
∠XBA
= 180° - 55° - 25°
= 100° (Interior angles, XY//BA)
Answer(s): (a) 25°; (b) 100°