The phrase "in high dudgeon" is an expression used to describe someone who is anger, irritated or offended. There are several synonyms that can be used to portray a similar emotion. One of those synonyms is "outraged", which describes a strong feeling of anger or shock in response to something unjust or wrong. Another synonym is "incensed", which conveys extreme rage or fury. "Fuming" is also a synonym that describes being in a state of extreme agitation or agitation. Additionally, the phrase "in a huff" may be used to convey irritation or annoyance, especially when someone is angry but trying to conceal it.