The figure is not drawn to scale. ZACD is a parallelogram. ∠DZO is 57° and ∠CAB is 31°. ZAB is an isosceles triangle and ZA = AB.
- Find ∠OBA.
- Find ∠ZDC.
(a)
∠AOZ = 57° (Alternate angles, ZD//AC)
∠AOB
= 180° - 57°
= 123° (Angles on a straight line)
∠OBA
= 180° - 123° - 31°
= 26° (Angles sum of triangle)
(b)
∠AZO = 26° (Isosceles triangle ZAB)
∠ZDC
= 180° - 57° - 26°
= 97° (Interior angles, ZA//DC)
Answer(s): (a) 26°; (b) 97°