Answer:
From the image, we can see that ∠AOC = ∠AOB + ∠BOC
We are given the following values:
∠AOC = 104
∠AOB = 7x + 30
∠BOC = 9x + 42
Plugging these values in the equation above:
∠AOC = ∠AOB + ∠BOC
104 = 7x + 30 + 9x + 42
104 = 16x + 72
16x = 32
x = 2
Now that we have the value of x, we can easily find the value of ∠BOC
We are given that:
∠BOC = 9x + 42
∠BOC = 9(2) + 42 (since x = 2)
∠BOC = 18 + 42
∠BOC = 60°
Therefore, ∠BOC is 60 degrees