A billiard ball of mass ‘M’ moving with velocity ‘v₁’ collides with another ball of the same mass but at rest. If the collision is elastic the angle of divergence after the collision is

When two bodies of same mass collide elastically, there velocities are exchanges along the line of collision.

So the first body will move perpendicular to the line of collision( common normal) and the second body will move along the line of collision.

So the angle of divergence after collision is 90^o.