Final answer:
Gawain convinces King Arthur to accept the challenge by emphasizing that his loss would be less significant than that of the King, showing selflessness and adherence to the chivalric code.
Step-by-step explanation:
Sir Gawain convinces King Arthur to let him accept the Knight's challenge by asserting his role and value at the court, highlighting that it would be less of a loss if he, rather than King Arthur, were to perish. He relies on his standing as a lesser knight and the nephew of the king to present his case as the most logical choice for accepting this perilous challenge.
By stepping forward, Gawain demonstrates his loyalty, courage, and honor, characteristics esteemed in Arthurian legend. His willingness to take on the challenge also upholds the chivalric code, which values bravery and the defense of one's liege lord above personal safety.
In the story 'Sir Gawain and the Green Knight,' Sir Gawain volunteers to take on the challenge to protect King Arthur's honor and reputation. He sees this as an opportunity to prove his worth as a knight and uphold the knightly code of chivalry.