Preposition ‘with’ is used to indicate a relationship between two people when they are related to an emotion, feeling or opinion. In the given sentence, the emotion conveyed is that of being vexed or annoyed. Therefore, the preposition ‘with’ should be used. The other prepositions given in the options are not appropriate in the given context.

Preposition ‘with’:
It is used to indicate a relationship between two people when they are related to an emotion, feeling or opinion.

For example:
I am happy with my job.
He is angry with his friend.

Therefore, the correct answer is Option A: with

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