Here is picture of the kitchen cabinet door that is just under the sink. The hinges are rusted and I want to replace these. However, I am not sure what these hinges are called and how to get the exact same ones again. What are these called?
Those are wide-angle hinges, definitely more than 110°.
Image from https://www.blum.com/us/en/products/hingesystems/clip-top-blumotion/programme/ (no affilations)
According to "A complete guide to hinge types," there's a strong possibility that what you have is called a full overlay hinge. A search with that term also returns a link to MyKnobs.com, largest collection of decorative hardware for something that looks pretty close to your image, a European Hinge 110 Degree Full Overlay:
There are various configurations for this type of hinge, including angle of opening and extension length.