Final answer:
The correct synonym for contiguous, in the context of states sharing a common boundary, is 'abutting.' 'Separated' and 'detached' are antonyms, not synonyms, of contiguous.
Step-by-step explanation:
The synonym for contiguous in the context of New Jersey and New York sharing a common boundary would be abutting. This term means that the states are next to each other or have a common border.
Adjourning is not a correct word, and it may be confused with adjoining, which does mean connected or next to. The word separated would be the antonym of contiguous, as it implies a distance or gap between objects or regions. Similarly, detached also indicates that the objects are separate or not joined, again an antonym of contiguous.