回答
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to announce one's resignation
「辞意を表明する」は
to announce one's resignation
と言います。
例:
He announced his resignation on the 1st of December.
「彼は12月1日辞意を表明した」
Everyone was surprised when he announced his resignation at the year end party.
「彼は忘年会で辞意を表明して、みんな驚いた」
ご参考まで!