"believed or thought to exist," 1580s, past-participle adjective from suppose (v.); often with the -e- pronounced, to distinguish it from the passive past tense supposed, now common in the sense of "to have a duty or obligation" (1859).
the supposed existence of ghosts
I'm supposed to be there at ten
he was supposed to go to the store
the supposed reason for his absence
support
supporter
supportive
supposably
suppose
supposed
supposedly
supposition
supposititious
suppository
suppress