<em>Arrogant</em> is the state of over-valuing one's own abilities and qualities, whereas <em>modest</em> refers to the opposite concept; to estimate other's abilities and achievements. This relationship means these terms are antonyms.
The answer to the question lies then on finding an antonym for <em>feeble, </em>which is the state of lacking strenght. The antonym for this term is <em>strong.</em>
