For a non relativist incoming particle m1,v1 making a non-head-on collision with a stationary particle m2, the angles between the two products (scattered incoming particle and ejected particle) are bound by the following equation :
Rewriting the equation :
The full demonstration is here.
Note an interesting case where m1= m2. As stated in the collision mechanics page, and for a non head-on collision, the resulting angle θ and φ are always 90° (π/2) :
