Consider the line passing through the center of the cue ball as the x axis. At the point of collision with the solid ball on the table, a line passing through the centers of the cue ball and the solid ball form a 45° angle with the X axis. Assume no external forces acting on the system and both balls have equal masses. At what angle will the cue ball move after the collision?

Answer 1

Momentum has to be conserved. So the cue ball has to go the direction such as to cancel the momentum to the 45 degree side of the first ball.
Most likely, the cue ball will go to the other side of the x axis at 45 degrees. That makes momentum conserved.

Answer 2

it’s 315