The Jargon File (version 4.4.7, 29 Dec 2003):

broket
 /broh'k@t/, /broh?ket`/, n.

    [rare; by analogy with ?bracket?: a ?broken bracket?] Either of the
    characters < and >, when used as paired enclosing delimiters. This word
    originated as a contraction of the phrase ?broken bracket?, that is, a
    bracket that is bent in the middle. (At MIT, and apparently in the Real
    World as well, these are usually called angle brackets.)


The Free On-line Dictionary of Computing (30 December 2018):

broket

    /broh'k*t/ or /broh'ket/ (From broken bracket)
   Either of the characters "<" or ">" when used as paired
   enclosing delimiters (angle brackets).

   [Jargon File]

   (1997-07-21)