Boil the angel hair in a large pot of salted water according to package directions. Reserve a little pasta water before draining.
In a large skillet, heat the olive oil over medium heat. Add the tomatoes and cook until they begin to burst. Stir in the garlic, artichokes, and olives, cooking for another 2–3 minutes.
Add the cooked pasta to the skillet. Pour in the lemon juice, salt, black pepper, and red pepper flakes.
Remove from heat. Toss with the fresh parsley and parmesan cheese. If it looks a bit dry, add a splash of that reserved pasta water.
