Can I use an adjective as a modifier at the beginning of a sentence?

The appositive meaning of "Angry" and "he" is clear and unambiguous so there is no reason to avoid the construction.

Cambridge dictionary

quotes an identical construct, albeit with a participial adjective "undaunted":

"Undaunted, we started to think about the problem."

You may also like the example of "Silent We Stood", which is the title of a novel by Henry Chappell.

It can be either and that depends on what the person wants to say. If they want to say that they smashed someone's head into a wall because they were angry, then the first sentence is the right one. if instead they simply want to say that they were angry while smashing someone's head into a wall, then the second sentence is what has to be used.