Angelo is placed in power after the Duke leaves and tightens the lax laws however uses them for his own purpose of trying to blackmail Isabella. However he is set up and gets his comeuppance, at the end of the play he is forced to marry Mariana however she saves him from execution.
Shakespeare uses Angelo in the play to display the primal desires of man and how a perfectly rational man can be completely changed by them. It would also appear that the Duke for saw that Angel would change in this way. We see how Angelo has changed on page 54 as the once strict temporary ruler is now ready to blackmail and commit a crime he is condemning another too.
Angelo is set to marry Mariana but her dowry is too small so he breaks off the engagement. Later on in the play he is tricked into sleeping with her as he thinks she is Isabella. So Shakespeare uses Mariana to show how Angelo is corrupt and create a sort of irony between Claudio and Angelo and without Mariana Angelo wouldn't be as ironic so she adds to his character. Isabella is used to a similar affect but also shows a key theme in relation to the clash between her and Angel which is suppressing the primal instincts in the extreme ( nuns ) vs. having no control over them ( Angelo and also Lucio).
In relation to the theme of the lax laws Angelo has the role of tightening them however the brothels only move and aren't completely destroyed showing that even with Angelo in power and not the Duke crime and deviance can not be stopped.
In relation to the theme of justice vs. mercy Angelo is heavily on the side of justice as he condemns Claudio to death and tries to tighten the law laws. However towards the end of the play after he has committed a crime himself he is willing to except the punishment of death so Shakespeare could be using this to portray him as not that much of a bad man after.
So overall Shakespeare created Angelo as a bad guy however redeems him at the end and he play a crucial role in the themes of the lax laws , justice vs. mercy and saints vs. sinners.