The figure is not drawn to scale. ZACD is a parallelogram. ∠DZO is 56° and ∠CAB is 25°. ZAB is an isosceles triangle and ZA = AB.
- Find ∠OBA.
- Find ∠ZDC.
(a)
∠AOZ = 56° (Alternate angles, ZD//AC)
∠AOB
= 180° - 56°
= 124° (Angles on a straight line)
∠OBA
= 180° - 124° - 25°
= 31° (Angles sum of triangle)
(b)
∠AZO = 31° (Isosceles triangle ZAB)
∠ZDC
= 180° - 56° - 31°
= 93° (Interior angles, ZA//DC)
Answer(s): (a) 31°; (b) 93°