Final answer:
The sentence in question makes use of ethos to appeal to the audience's sense of moral reasoning, contrasting the humble and persistent petitions with the unfair responses received.
Step-by-step explanation:
The rhetorical device most clearly used in the statement 'Redress in the most humble terms: our repeated petitions have been answered only by repeated injury' is an appeal to ethos.
This is because the speaker is establishing credibility and moral character by highlighting the humbleness and persistence of their petitions, and contrasting that with the unfair treatment they have received in response. While logos (appeal to logic) does play a role in persuasive writing, the specific phrasing here is more aligned with ethos, demonstrating the virtue and fairness of the petitioner in contrast to the unjust actions of the one they petition to.