Here's how it works:
* Contemptuous is an adjective, meaning "showing or feeling contempt."
* Contempt is a noun, meaning "the feeling that a person or a thing is worthless or despicable."
For example:
* Contemptuous gaze: He looked at her with a contemptuous gaze.
* Feeling contempt: She felt contempt for his shallowness.
* Act of contempt: His actions were an act of contempt for the law.