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late 15c., past participle adjective; see perplex. A case of a past participle form attested centuries before the verb (perplex isn't recorded until 17c.). Related: Perplexedly; perplexedness.
late 14c. as an adjective, "perplexed, puzzled, bewildered," from Latin perplexus "involved, confused, intricate;" but Latin had no corresponding verb *perplectere. The Latin compound would be per "through" (see per) + plexus "entangled," past participle of plectere "to twine, braid, fold" (see complex (adj.)).
The form of the English adjective shifted to perplexed by late 15c., probably to conform to other past participle adjectives. The verb is latest attested of the group, in 1590s, evidently a back-formation from the adjective. Related: Perplexing, which well describes the history of the word.