The molecules CH4 and CH3Cl both have tetrahedral shapes. Why is CH4 nonpolar whereas CH3Cl is polar?

Because in CH4 the valence electrons of Carbon are being pulled away from the nucleus with the same force (since all hydrogen has the same electronegativity). So charges are equally distributed throughout the atom and the atom is non-polar. In CH3Cl Cl has a different electronegativity than H, so charges aren't equally distributed and therefore the molecule is polar.