The figure is not drawn to scale. ZACD is a parallelogram. ∠DZO is 59° and ∠CAB is 30°. ZAB is an isosceles triangle and ZA = AB.
- Find ∠OBA.
- Find ∠ZDC.
(a)
∠AOZ = 59° (Alternate angles, ZD//AC)
∠AOB
= 180° - 59°
= 121° (Angles on a straight line)
∠OBA
= 180° - 121° - 30°
= 29° (Angles sum of triangle)
(b)
∠AZO = 29° (Isosceles triangle ZAB)
∠ZDC
= 180° - 59° - 29°
= 92° (Interior angles, ZA//DC)
Answer(s): (a) 29°; (b) 92°