The Collaborative International Dictionary of English v.0.48:

Angriness \An"gri*ness\, n.
   The quality of being angry, or of being inclined to anger.
   [1913 Webster]

         Such an angriness of humor that we take fire at
         everything.                              --Whole Duty
                                                  of Man.
   [1913 Webster]

WordNet (r) 3.0 (2006):

angriness
    n 1: the state of being angry [syn: anger, angriness]