The figure is not drawn to scale. ZACD is a parallelogram. ∠DZO is 55° and ∠CAB is 31°. ZAB is an isosceles triangle and ZA = AB.
- Find ∠OBA.
- Find ∠ZDC.
(a)
∠AOZ = 55° (Alternate angles, ZD//AC)
∠AOB
= 180° - 55°
= 125° (Angles on a straight line)
∠OBA
= 180° - 125° - 31°
= 24° (Angles sum of triangle)
(b)
∠AZO = 24° (Isosceles triangle ZAB)
∠ZDC
= 180° - 55° - 24°
= 101° (Interior angles, ZA//DC)
Answer(s): (a) 24°; (b) 101°