Answer:
Alex is going bowling after lunch; that explains his goofy shoes.
The sentence that uses both a participial an an infinitive phrase is 3. Annoying me into a rude awakening, the alarm continued to buzz loudly in my ear.
The participial phrase is <em>annoying me into a rude awakening, </em>and the infinitive phrase is <em>to buzz loudly in my ear.</em>
