verb 1she was perplexed by her husband's moodiness PUZZLE , baffle, mystify, bemuse, bewilder, confound, confuse, nonplus, disconcert, keep someone guessing, dumbfound, throw, throw/catch someone off balance, get, exercise, worry, befuddle, fuddle, addle, fog; informal flummox, be all Greek to, discombobulate, stump, bamboozle, floor, beat, faze, make someone scratch their head, fox; archaic wilder, distract, gravel, maze, pose, cause to be at a stand. See AWKWARD SYNONYMS at puzzle.
2it is possible to perplex the question COMPLICATE , make complicated/complex, confuse, make obscure/unclear, obscure, obfuscate, cloud, befog, blur, muddle, mix up; muddy the waters; rare ravel.