Answer :
The presence of a supermassive black hole can be deduced from observations of the high speeds of orbiting stars & gas, as evidenced by broad emission lines. The central mass can be estimated from Kepler's 3rd law.
Astronomers can observe clusters of stars and gas moving around the center of the galaxy and use these movements to infer the mass of the central black hole. We measure the motion of stars, vortices of gas around them, and now, thanks to the Event Horizon Telescope Imaging Project the diameter of black holes.
Astronomers at the Max Planck Institute for Astronomy have successfully tested a new method for determining the mass of extreme black holes in quasars for the first time. This method is called spectrometry and is based on measurements of radiation emitted from gas near supermassive black holes. By tracking the movement of gas and dust near the black hole that is attracted to the black hole's mass, we can measure the mass of the black hole.
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