He has the presence of mind to answer these embarrassing questions.
an equivocal statement; the polling had a complex and equivocal (or ambiguous) message for potential female candidates; the officer's equivocal behavior increased the victim's uneasiness; popularity is an equivocal crown; an equivocal response to an embarrassing question.
Particularly when asked a difficult or embarrassing question, the person may blush, with redness appearing across the face and sometimes into ears and down the neck.
He tried to evade the embarrassing question.
Don't ask embarrassing questions.
The reporter wanted to heckle the candidate with those embarrassing questions.
He answered these embarrassing questions with presence of mind.