If m< AOD = 135 degrees, what is m<BOD

45°
Line AB and Line CO is perpendicular because it formed a right angle.
If ∠AOD = 135°, and ∠AOC = 90° because it's a right angle, then...
∠AOD - ∠AOC = ∠DOC
135 - 90 = 45
Then, ∠COB is also a right angle because lines AB and CO are perpendicular.
So, if ∠COB = 90, and ∠DOC = 45°, then...
∠COB - ∠DOC = ∠DOB
90 - 45 = 45°
Therefore, the measure of ∠BOD is 45°.