To what extent is Angelo's fall tragic in Measure for Measure?

What exactly do you mean by "tragic"? Certainly he does
suffer a massive fall from grace. At the beginning of the play he is presented as if he
were characterised by self-control. Others consider that he adheres to a strict moral
code. However, when the Duke gives him an opportunity to have absolute power, he shows
himself to be just as corruptible and open to temptation as anyone else. Note how
Isabella foreshadows his fall when protesting against the sentence imposed on her
brother:

If
he had been as you, and you as he,

You would have slipp'd
like him;

But he, like you, would not have been so
stern.

Of course, when he
does fall through sleeping with Mariana, he then tries to cover his crime with
hypocrisy, leading Isabella to denounce him as a "devil" inspite of the fact that he is
"outward-sainted."

Thus he is not a character that excites
much sympathy during the course of the play. In particular, once he has decided to
proposition Isabella, it seems in his own mind as if there is no turning back. He says
"I have begun, and now I give my sensual race the rein" as he goads himself on into
ever-further acts of wrongdoing against Isabella and her brother to gain her
virtue.

Some argue that the tragic flaw of Angelo is his
very lack of self-knowledge. By considering himself to be morally above the people that
he rules he is unaware of how he is related to them through the same temptations that
they all suffer, and also this ignorance leaves him more open to those temptations when
they do come, precisely because he believes he is above them. This is a position that is
reversed when he is forced to confess and acknowledge his
guilt.

Thus Angelo does have his tragic flaw of believing
himself to be morally superior to everyone else, wherein lies the seeds of his
destruction. However, whether we feel sorrow and pity for his fall is another matter. I
certainly feel he got what he deserved, thus he is exempted from being seen as
tragic.