Yes, "Why are you angry with me?" is a correct and grammatically sound sentence. It is a question asking someone about the reason for their anger towards the speaker.
The sentence structure is as follows:
- "Why" is an interrogative adverb that introduces a question asking for the reason or cause.
- "are" is the present tense of the verb "to be," used with the pronoun "you."
- "you" is the pronoun referring to the person being addressed.
- "angry" is the adjective describing the emotional state of the person being addressed.
- "with me" is a prepositional phrase indicating the object of the anger, specifying that the anger is directed at the speaker.
Overall, it's a clear and appropriate way to inquire about someone's feelings towards you.