The figure is not drawn to scale. XYAB is a parallelogram. ∠BXO is 59° and ∠AYZ is 27°. XYZ is an isosceles triangle and XY = YZ.
- Find ∠OZY.
- Find ∠XBA.
(a)
∠YOX = 59° (Alternate angles, XB//YA)
∠YOZ
= 180° - 59°
= 121° (Angles on a straight line)
∠OZY
= 180° - 121° - 27°
= 32° (Angles sum of triangle)
(b)
∠YXO = 32° (Isosceles triangle XYZ)
∠XBA
= 180° - 59° - 32°
= 89° (Interior angles, XY//BA)
Answer(s): (a) 32°; (b) 89°