Anger is a common human emotion and is expressed in various ways. However, the term "angriness" may sound a bit informal or colloquial. There are many synonyms for this word that can be used in more formal or professional settings. Some of these synonyms include "irritation," "fury," "outrage," "indignation," "exasperation," and "resentment." It's essential to choose the right synonym based on the context and the level of intensity of the emotion being expressed. Each of these words captures a slightly different aspect of the emotion and can be used in different situations to convey the appropriate sentiment.