What kind of repairs are prudent for a ridge board damaged by a falling tree?
As this is a 1x board, I take it this is a ridge board and not a true beam. If this is in an attic and there are ceiling joists below the rafters making a triangular structure, the ridge board has little structural value, it just serves to tie the rafters together, it does not support any vertical loads. In that case, nail/gluing patch blocks on each side will suffice as a repair.

If this is a true load bearing beam, (unlikely since it appears to be a 1x board) it would have needed to be replaced in it's entirety unless a licensed engineer could design a proper repair to the beam.