Does the photoelectric effect support the wave theory of light? the particle theory of light?

Yes

Explanation:

The photoelectric effect is a phenomenon which show that electric can be emitted from a material or a thin metal sheet when  light of appropriate frequency fall it.  For example when X-rays is allowed to fall on the surface of a thin sheet of metal like gold, the X-ray not only produces diffraction pattern but also acting like particles they may collide with the metal and eject electrons which is the photoelectric effect.

Experiment have also shown that matter or light behave as  particle observable phenomenon such as reflection,  refraction, diffraction can be interpreted by assuming that light behaves as a wave.

As such the wave and particle nature of light makes light to have a dual properties. light behave either as a wave or a particle but not as both at the same time