From the figure we know that ∠AOC and ∠AOD form a linear pair.
It can also be written as
∠AOC + ∠AOD = 180o
By substituting the values
50o + ∠AOD = 180o
∠AOD = 180o – 50o
By subtraction
∠AOD = 130o
According to the figure we know that ∠AOD and ∠BOC are vertically opposite angles
So we get
∠AOD = ∠BOC = 130o
According to the figure we know that ∠AOC and ∠BOD are vertically opposite angles
So we get
∠AOC = ∠BOD = 50o