Answer:
The type of phrase is: participial.
Explanation:
In "Rebelling against the British, the Daughters of Liberty made their own tea instead of buying it from England," the phrase "rebelling against the British" begins with a present participle. The present participle is formed by adding -ing to the base form of a verb, in this case, "rebelling". What we have is, thus, a participial phrase, consisting of a participle and complements.
Participial phrases function as adjectives, modifying a noun in the sentence. In this case, the phrase "rebelling against the British" refers to the Daughters of Liberty, giving us more information about them. Now we know that they were defying the British when they made their own tea.