The most common and most likely answer to this crossword clue is the 10 letter word AGGRAVATED
I've seen this crossword clue in The Times
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More clues leading to the result AGGRAVATED
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The straight part
We know that "Very annoyed" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case very annoyed = aggravated.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does AGGRAVATED mean?
AGGRAVATED verb- To make (an offence) worse or more severe; to increase in offensiveness or heinousness.
- (by extension) To make worse; to exacerbate.
- To give extra weight or intensity to; to exaggerate, to magnify.
- To pile or heap (something heavy or onerous) on or upon someone.
- To exasperate; to provoke or irritate.
- Having been the subject of aggravation; frustrated and angry.