How did the first image of a black hole test the general relativity? Recently, the event horizon of the black hole at the center of M87 was directly imaged by the EHT.
My college professor said this could serve as another test of the accuracy of general relativity. How does the observation test the GR, in detail? And compared with the test of LIGO?
 A: Prior to the EHT images, there were no "zoomed in views" of a black hole candidate.
One of the predictions made by GR is that light travelling in the spacetime metric close to a black hole should follow strongly curved paths. In fact there is a radius, which is a small multiple of the Schwarzschild radius, where if we trace a detected light ray back, it should have arisen after orbiting the black hole one or more times. In contrast, light that came closer to the black hole than this would have fallen in and not escaped. Therefore a clear prediction of GR is that there should be a shadow with a bright ring around it, and the radius of the ring should be a precise multiple of the Schwarzschild radius, given by $2GM/c^2$.
Since, the mass $M$ of the black hole had already been estimated from the observed dynamics of gas orbiting the black hole, there was a reasonably good prediction of the radius of the bright ring.
That the observed radius agrees with this prediction is a test that GR has passed, though it is fair to say it is not a particularly precise test (the error bars are of order 10-20%).
Footnote: The predicted radius (and exact shape) of the ring does depend (at the 10% level) on the spin of the black hole too.
A: 
My college professor said this could serve as another test of the
  accuracy of general relativity

Given that GR has already been tested to some ungodly precision, I think the answer is "it can't".
I mean, you can say that it proves that GR is right about BH's, and you could say that's a test of GR, and maybe that's "the accuracy" he's referring to.
