The Collaborative International Dictionary of English v.0.48:

Vexed \Vexed\, a.
   1. Annoyed; harassed; troubled.
      [1913 Webster]

   2. Much debated or contested; causing discussion; as, a vexed
      question.
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The Collaborative International Dictionary of English v.0.48:

Vex \Vex\ (v[e^]ks), v. t. [imp. & p. p. Vexed (v[e^]kst); p.
   pr. & vb. n. Vexing.] [F. vexer, L. vexare, vexatum, to
   vex, originally, to shake, toss, in carrying, v. intens. fr.
   vehere, vectum, to carry. See Vehicle.]
   1. To toss back and forth; to agitate; to disquiet.
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            White curl the waves, and the vexed ocean roars.
                                                  --Pope.
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   2. To make angry or annoyed by little provocations; to
      irritate; to plague; to torment; to harass; to afflict; to
      trouble; to tease. "I will not vex your souls." --Shak.
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            Ten thousand torments vex my heart.   --Prior.
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   3. To twist; to weave. [R.]
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            Some English wool, vexed in a Belgian loom.
                                                  --Dryden.
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   Syn: See Tease.
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WordNet (r) 3.0 (2006):

vexed
    adj 1: troubled persistently especially with petty annoyances;
           "harassed working mothers"; "a harried expression"; "her
           poor pestered father had to endure her constant
           interruptions"; "the vexed parents of an unruly teenager"
           [syn: annoyed, harassed, harried, pestered,
           vexed]
    2: causing difficulty in finding an answer or solution; much
       disputed; "the vexed issue of priorities"; "we live in vexed
       and troubled times"