Angrily means in a way that shows anger. Shout angrily, angrily denied it, gesture angrily.
It is a favourite of newspapers, where a politician angrily denied something rather than simply denying it. The adverb reports how a thing was done rather than what was felt, which is a distinction worth keeping.
1adverbangrilyIn a way that shows anger.
“"Get out of my kitchen!" she shouted angrily.”
angrily is a manner.
From angry plus -ly, with angry from Old Norse angr, grief or trouble.
Middle English
angrily
English, today
angrily
From Middle English angrily, equivalent to angry + -ly.
Etymology from Wiktionary, CC BY-SA