The figure is not drawn to scale. XYAB is a parallelogram. ∠BXO is 54° and ∠AYZ is 31°. 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° - 31°
= 23° (Angles sum of triangle)
(b)
∠YXO = 23° (Isosceles triangle XYZ)
∠XBA
= 180° - 54° - 23°
= 103° (Interior angles, XY//BA)
Answer(s): (a) 23°; (b) 103°