“I am angry to die” or “I am angry to death”
I am full to die.
I meant to say, "I might die because I am full."
Is this a correct expression?
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No, this isn't correct. I'm assuming that your sentence means that you've eaten far too much dinner, that you've got a serious stomachache, and that you don't want to stick your finger down your throat to relieve the pain, and that therefore you want to die. I felt that way when I gave myself alcohol poisoning one New Year's Eve.
You might want to say I'm so full that I might die.
Google finds just three examples of this phrase, two in a blog and one in a Chinese site. In these cases it seems to mean "I am so full I could die", or more idiomatically, "I am full to bursting."
"I am full to die" is not grammatical these days; the construction is at best archaic and may be obsolete ("I am angry to die" = "I am so angry I could die").
Full to needs a noun — to is a preposition. Something can be full to the top, full to overflowing (overflowing is a gerund), full to bursting.