Lad in RAC angered churchman (8)

I believe the answer is:

cardinal

I'm a little stuck... Click here to teach me more about this clue!

'churchman' is the definition.
(I have seen 'Senior churchman' mean 'cardinal' so perhaps 'churchman' could also mean 'cardinal')

'lad in rac angered' is the wordplay.
'lad in rac' anagrams to 'CARDINAL'.
But, I am not clear how this is indicated.

Can you help me to learn more?

(Other definitions for cardinal that I've seen before include "Senior churchman - bird" , "Word to describe one or two" , "Principal - churchman" , "of prime importance" , "cleric" .)

I've seen this clue in The Sun.

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