I will not use three letters to describe an angle, i'll use one.
Let O be angle BOC
Let be angle BAC
Let C be angle ACB
Let B be angle ABC
We want to find angle O (the red angle) in terms of
Remember that all angles in a triangle add up to , and that bisecting an angle means dividing it into two equal parts.
So, for we must have that:
Now for we must have:
Now substitute the expression for B + C from equation (1), we get: