Perfectly happy with rags, perhaps (4)

I believe the answer is:

glad

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'perfectly happy' is the definition.
'glad' can be an answer for 'happy' (synonyms). I am not certain of the 'perfectly' bit.

I cannot understand how the remainder of the clue works.

Can you help me to learn more?

(Other definitions for glad that I've seen before include "Joyful" , "Contented" , "Pleased, delighted" , "Made up" , "Feeling happy" .)

I've seen this clue in the Evening Standard.

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