Lines 82–87: what is the effect of king mentioning his nobel prize?

Between lines 82–87 the effect of Martin Luther King mentioning his Nobel Prize is to explain why he is against the Vietnam war after people started questioning his opinion on the ending of the Vietnam war. In his speech, he addresses how the poor people in Vietnam have been forced to take part in the war as their houses are being torched leaving them homeless. The mentioning of his Nobel prize is to justify his commission for "the brotherhood of man."  which made civil rights to condemn him for his speech as the war was against his commission.

it exposes the hypocrisy of religion and christian supporters of slavery

there is no passage what do you mean?

give me the passage and i will answer your question