'absolutely angry' is a correct and usable phrase in written English.
You can use it when you want to emphasize how angry you are, for example "I am absolutely angry that I have to do this project."
Ghassan Mutar, an Awakening leader in the neighborhood, said Monday that "people will be absolutely angry" if the government did not deliver on its assurances.
D'Hooghe, speaking at the Leaders in Sport conference in London, said: "We [Fifa's executive committee] are absolutely angry on that situation.
"I feel absolutely angry to the core of my being that children who deserve to be properly educated and have their needs met are not having their needs met – and that's across the academic and social needs range," he says.
(Explanation: Yes, you're right to be angry, absolutely.
Sillitoe describes it as "an extended essay about integrity" and Courtenay ("I was absolutely not an angry young man") also provides pertinent comment on an exemplary DVD.
Much – even most – of the time, they're prompted by people being sexist or racist or in other ways ignorant or unjust, which is absolutely worth getting angry about.
"Everybody is absolutely frustrated; everybody is angry.
"The folks that are angry are absolutely justified in their anger".
She finds reasons to be angry about absolutely everything, even at one point forcing a paddy about contestants using their hands during a photoshoot.
"I would say to people yes, you are absolutely entitled to be angry, but we've got to be very careful to ensure that we do not allow our anger to make a bad situation worse".
"Ought I to light a joint?" Jonathan asked — now a trace of his Southern diction emerged — and William said, "Absolutely," but Sarah, still angry, said, "Save it for later".
