Step-by-step explanation:
In the sentence "I'm really annoyed with one of my co-workers," the word "annoyed" is (A) a Present participle.
Present participles are verb forms that end in "-ing" and can function as adjectives. In this sentence, "annoyed" describes the state or feeling of the subject ("I") and modifies the pronoun "I." It indicates that the person is experiencing annoyance with one of their co-workers.