I'm impressed at being angry (5)

I believe the answer is:

irate

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'being angry' is the definition.
(irate can mean angry or annoyed)

'i'm impressed' is the wordplay.
'i'm' becomes 'i' (I've seen this in other clues).
'impressed' becomes 'rate' (I can't justify this - if you can you should give a lot more credence to this answer).
'i'+'rate'='IRATE'

'at' acts as a link.

Can you help me to learn more?

(Other definitions for irate that I've seen before include "Infuriated" , "ranting" , "Fuming" , "Ticked off" , "Narked" .)

I've seen this clue in The Sun.

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