What appeal are the drafters of the declaration using when they say they are prudent and reasonable men?

They are using ethos. Ethos, as a rhetorical appeal, is a mode of persuasion that uses a source or a figure that shows credibility, expertise, prestige or character to convince an audience that the information is reliable. When the drafters of the Declaration of Independence say they are prudent and reasonable men, they are doing so to convince the audience that what they are saying is also reasonable and worth paying attention to.

you did not put the article. so i cannot answer the question.