Answer:
The sentence that uses both a participial and an infinitive phrase is "Annoying me into a rude awakening, the alarm continued to buzz loudly in my ear."
Explanation:
There are both a participial and infinitive phrase in the complete sentence number 3, the participial phrase is "Annoying me into a rude awakening" where "Annoying" is the participle. The infinitive clause is " the alarm continued to buzz loudly in my ear." where "to buzz" is the infinitive verb in the sentence.