The figure is not drawn to scale. XYAB is a parallelogram. ∠BXO is 58° and ∠AYZ is 32°. XYZ is an isosceles triangle and XY = YZ.
- Find ∠OZY.
- Find ∠XBA.
(a)
∠YOX = 58° (Alternate angles, XB//YA)
∠YOZ
= 180° - 58°
= 122° (Angles on a straight line)
∠OZY
= 180° - 122° - 32°
= 26° (Angles sum of triangle)
(b)
∠YXO = 26° (Isosceles triangle XYZ)
∠XBA
= 180° - 58° - 26°
= 96° (Interior angles, XY//BA)
Answer(s): (a) 26°; (b) 96°