Final answer:
The speaker in Martin Luther King's 'Letter from Birmingham Jail' is using ethos as the type of appeal.
Step-by-step explanation:
The speaker in Martin Luther King's 'Letter from Birmingham Jail' is using ethos as the type of appeal. Ethos refers to the credibility and trustworthiness of the speaker. In the passage, King acknowledges the good intentions of the recipients of the letter and expresses his willingness to engage in patient and reasonable discussion, which helps establish his credibility and build trust with the audience.