Lets say you drilled pilot holes for two angle brackets on each rear leg. Thats 8 screws in each rear leg, or 16 rather large borer holes in the portion of the chair which receives the greatest stress and needs to give the greatest strength. Not only will these holes weaken the chair, but the brackets over time will become loose and the brackets will begin to act like chisels damaging the wood while the screws will act like files as they further enlarge the holes.
Well designed and made chairs utilize wooden joints held together by glue to make two or more parts into a unitary whole. The problem with metal fixings, is that wood and meal have different hardnesses and flexibility, eventually working against each other, with the wood usually losing. Well made and glued joints will stay fixed (in most cases) unless the chair suffers catastrophic damage by physical force, water damage, etc.
The proper way to return your wooden dining chair to full usability, is to take it apart as completely possible, then to clean all the joints. Then apply glue to all joining surfaces and clamp under pressure for 24 hours. Or, if you like, contact us and we will do that work for you, touching up any visible damage once the repair has made made.