What would be the correct completion: After announcing his resignation, he said that he had done nothing improper?

The statement "He went on to deny that he had done anything improper" effectively follows the context given in the question. This option indicates a continuation of his defense after the announcement of his resignation. It aligns with the narrative that he is asserting his innocence regarding any wrongdoing, thereby reinforcing his claim that his actions were appropriate.

The phrasing "went on to deny" suggests that this denial was part of a broader statement or a response to questions raised about his conduct, which is plausible in the context of a resignation announcement. It captures the proactive nature of his denial and conveys a sense of determination to clarify his position.

In contrast, the other options introduce elements that either suggest a lesser degree of engagement with the denial or imply an absence of denial. For instance, "volunteered to deny" might suggest that the act of denying was done without prompting, which may not fully convey the gravity of the situation. "Stood up to deny" could imply a confrontational approach that isn’t reflected in the original statement. Lastly, "failed to deny" introduces ambiguity and contradicts the assertion of innocence implied in the resignation announcement. Thus, "He went on to deny that he had done anything improper" is the most coherent and contextually appropriate completion