Remark
Every triangle has 180 degrees. The given triangle is ABC. It can be represented as
A + B + C =180 degrees.
<BOC = 180 - 1/2B - 1/2C The angle bisectors form a triangle with the base.
<BOC = 180 - 1/2(B + C)
B + C = 180 - A from the first relationship.
<BOC = 180 - 1/2(180 - A) Remove the brackets.
<BOC = 180 - 1/2*180 + A/2
<BOC = 180 - 90 + A/2
<BOC = 90 + A/2 which is what we were asked to prove.