How was the evidence discovered supporting the theory that a supermassive black hole is at the center of our Galaxy?
Evidence for a supermassive black hole at the centre of the galaxy is the motion of stars.
Observations of stars known to be near the centre of galaxy showed that they are moving fast. The motions of these stars showed that they were orbiting around a central body.
The orbital periods of the stars showed that they are orbiting around a massive object of around 4 million times the mass of the Sun. The orbits also showed that the object must be quite small. It is around the size of our Solar System.
The only thing which can be so massive and yet so small is a supermassive black hole. Observations of other galaxies has shown that they too contain a supermassive black hole at their centres.
Recent evidence has shown that the mass of the supermassive black hole at the centre of a galaxy is related to the mass of the galaxy itself. There are theories that the supermassive black hole controls star formation and that it drives the evolution of the galaxy.