ASP.NET MVC is a server-side framework; it doesn't care what JavaScript libraries do you use. AngularJS is a client-side library, which doesn't care what server-side technology powers the website—it can be Python, ASP.NET MVC, or even the plain old bunch of static HTML files stored directly on disk.
ASP.NET MVC and AngularJS are both compatible, and there are plenty of projects out there which use them together.
Do you need to use both? Not really. It depends entirely on the needs of your project.
If your website is dynamic, you have to use some server-side scripting. You could use ASP.NET, and the fact that you are using AngularJS won't make your server-side code more MVC. If you want to be able to structure your server-side application as MVC, you'll rather pick ASP.NET MVC.
Similarly, the fact that you are using ASP.NET MVC doesn't imply anything about the structure of your client-side code. You can put all your JavaScript in a single file without any thought about the structure and be happy with that (until the project starts to grow). Here again, AngularJS presents itself as a way to structure your application on client-side.
Side note: you tagged your question ASP.NET MVC 3. Unless this is a legacy project you have to maintain or you have specific constraints when hosting the application on legacy servers which weren't updated for the last four years, you could use ASP.NET MVC 4 or 5 instead.