Which of the following sentences has correct use of prepositions? (A) I was angry at my results so I spoke with the teacher. (B) I was angry with my results so I spoke to the teacher.

here results are not a person so it is a different question

  • The object of the anger here isn't a person (so Speak to or speak with doesn't seem appropriate, even if speak were the same as being angry); and it's not a situation either. The object of the anger is a thing. The "Angry with* question doesn't really cover that, I feel.
    – Andrew Leach
    Apr 1 '17 at 9:39

You are angry neither with nor at your results, but angry about / for the results. See examples at Oxford Learner's Dictionaries:

angry with/at somebody about/for something:

I was very angry with myself for making such a stupid mistake.

The passengers grew angry about the delay.

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