I'm in the same boat. My four year old wants to ask questions all day-- but these aren't interesting, because these are questions he already knows the answer to. "Was Tyranosaurus Rex a meat eater?" (hell, yeah!) "Did diplodicus die? Did triceratops die? ("Dude, they all died. Every single dinosaur died.Millions of years ago.") "Can we eat dinosaur meat?" ....notice a theme?
If I did not actively ignore my son, I would go crazy. I listen for when he asks "interesting questions" (questions he hasn't asked a million times), and then stop and answer those.
What I have found works for me is to sometimes say "You know, right now, Mama needs to think about X (washing dishes, cooking, whatever it is you want to do), and so I'm going to be quiet for a while. If you want to keep talking, you can play (over there, bedroom, living room). I'll let you know when I'm ready to talk again."
There's something to be said for teaching kids context. As I said, I've been through this with my son. His habit of introducing "done to death" topics with his preschool peers has been met with some exclusion. I even heard another child tell him, rolling their eyes "We know that already. You always tell us that." Made me sad, but made me understand MY part in his habit of doing this. I love Kiddo so much, and realized that my answering/indulging these repetitive questions was actually setting a bad example for him.
Is yours by chance an "only"? I ask this because mine is, and my experience is that only children are answered a lot more, mainly because when they are home with us, it's just us and them. When they talk, we assume they are talking to us.
I hope it gets better and don't feel badly for being frustrated. I know that if I hear "Did plant eaters eat meat eaters?" again and again, I might go nuts too.