'obtuse' originates from Latin, specifically the word 'obtusus', where 'obtus-' meant 'dull' or 'blunt'. 'apex' originates from Latin, specifically the word 'apex', where 'apex' meant 'summit' or 'tip'. The compound 'obtuse-apexed' is a modern English botanical formation combining these elements with the adjectival suffix '-ed'.

'obtuse' changed from Latin 'obtusus' to Old French 'obtus' and then into Middle/Modern English as 'obtuse'. 'apex' passed from Classical Latin 'apex' into Late Latin and was later borrowed into English. The compound form 'obtuse-apexed' developed later in technical botanical descriptions (19th–20th century).

Initially, 'obtuse' meant 'blunt' and 'apex' meant 'tip'; combined, the modern compound specifically denotes a 'blunt or rounded apex', a narrower botanical sense than the separate words.