Make bisectors of angles a and b, respectively, and set them at point D.

Then in triangle ABD, angle BAD+ angle ABD+ angle ADB = 180.

Another angle BAD+ Angle ABD= 1/2 Angle BAC+ 1/2 Angle ABC= 1/2 (Angle BAC+ Angle ABC) = 45.

So the angle ADB = 135, and the other intersection angle is 45, so choose C.

answer the question

The level is low, I can't put the picture below, sorry. I wonder if this explanation is satisfactory?