The galaxy could be measured a couple of ways. One way is to simply to measure the optical emission which is the luminosity of a galaxy and to determine the average mass of the star in the galaxy. This will eventually lead to an estaminate for the mass of the galaxy if all of the luminosity is in fact due to the stars and all material radiates in a similar manner. The second way is to determine masses is to use our knowledge of physics. All mass is expected to interact gravitationally whether or not we can see it. We should be able to measure the mass with our eyes by their effects.