Anger? Irrational figure quite losing it (5)
I believe the answer is:
pique
'anger?' is the definition.
(pique is a kind of anger)
'irrational figure quite losing it' is the wordplay.
'irrational figure' becomes 'pi' (pi is an irrational number).
'losing' is a deletion indicator.
'quite' with 'it' taken out is 'que'.
'pi'+'que'='PIQUE'
(Other definitions for pique that I've seen before include "Stimulate (one's curiosity)" , "Resentment at a slight" , "Angry resentment" , "Resentful feeling" , "Offence taken" .)