How does the light waves/photons interact with the atoms on the reflecting surface to ensure that the angle of incidence = angle of reflection?
Think of an incoming classical electromagnetic plane wave. It has a definite phase at every atomic site. The electric field of that wave shall induce forced oscillations of atoms (in case they're charged) and/or electrons (which we'll consider localized at atomic sites for simplicity). So you produce induced oscillating dipoles, and each oscillator oscillates with a well-defined (and the same for each oscillator of the same kind) relative phase with respect to the local phase of the plane wave.
Now think of these oscillators as radiating Hertz' dipoles. Again, the radiated field can be computed. now add this up respecting correctly all phases. in the solid, add this up with the original plane wave to get the resulting travelling wave (including change of phase velocity and direction (refraction)) and outside the solid to obtain the reflected wave (with the known rule for the reflected angle).
Please see this reference as a formalization of Kai Fauth's answer:
https://www.researchgate.net/publication/308794196_The_Atomic_Origin_of_the_Reflection_Law
Article The Atomic Origin of the Reflection Law
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