On a moving plane mirror, incident ray forms an angle of $60^{\circ }$, then what will be the reflected angle?

According to the fundamental Law of Reflection, the angle of incidence ($i$) is always equal to the angle of reflection ($r$) relative to the surface normal:
$$\angle r=\angle i=60^{\circ }$$
The instantaneous angle of reflection is determined by the angle of incidence at that moment.