'angle-preserving' originates from Modern English as a compound of 'angle' and the present participle 'preserving'. 'angle' traces back to Old English 'angel' (from Proto-Germanic *angulaz) meaning 'hook, corner', and 'preserve' originates from Latin 'praeservare', where the prefix 'prae-' meant 'before' and 'servare' meant 'to keep'.

'angle' came into English from Old English 'angel' and via Middle English remained 'angle'; 'preserve' comes from Latin 'praeservare' -> Old French/Medieval Latin forms -> Middle English 'preserven' and the modern verb 'preserve'; the compound 'angle-preserving' is a Modern English formation used especially in mathematical contexts to describe maps or transformations that 'preserve angles'.

Individually, 'angle' originally meant 'hook' or 'corner' and 'preserve' meant 'to keep'; when combined in Modern English as 'angle-preserving' the meaning specialized to 'keeping/preserving angles', now used chiefly in mathematics to mean 'conformal' or 'angle-preserving'.