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The angle defined by joining a line from the centers of the balls must be important. But do they follow this angle when viewed in the rest frame of one of the balls or in the CM frame?

The spheres are hard and friction is ignored. I've tried googling a lot. All of the examples include the final angle as given.

Please if give an argument for the answer as well. Thanks in advance.

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This is actually an extremely complicated problem if you try to model all the physically relevant effects. There is friction between the balls and between each ball and the felt. The incident ball may or may not be rolling without slipping. Even if the incident ball was rolling without slipping, both balls may be slipping after the collision. Related: physics.stackexchange.com/q/62619 –  Ben Crowell Oct 1 '13 at 0:00

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