AngularJS is more associated with the single page application paradigm, and as such, doesn't benefit much from server-side technologies that render markup. There is no technical reason that precludes you using them together, but in a practical sense, why would you?
An SPA retrieves the assets it needs (JS, CSS, and HTML views) and runs on its own, communicating back to services to send or retrieve data. So, a server-side technology is still necessary for providing those services (as well as other means such as authentication and the likes), but the rendering parts are largely irrelevant and not particularly useful because it's a duplication of efforts, except MVC does it on the server side and Angular does it on the client. If you're using Angular, you want it on the client for best results. You can make Angular post HTML forms and retrieve partial views from MVC actions, but you'd be missing out on the best and easiest features of Angular and making your life harder.
MVC is pretty flexible and you could use it to service calls from an SPA application. However, WebAPI is more finely tuned and a bit easier to use for such services.
I've written a number of AngularJS applications, including a couple that migrated from pre-existing WebForms and MVC applications, and the ASP.NET aspect evolves towards a platform for delivering the AngularJS app as the actual client, and for hosting the application layer the client communicates to via REST (using WebAPI). MVC is a fine framework, but it usually finds itself without a job in these sorts of applications.
The ASP.NET application becomes another layer to the infrastructure, where its responsibilities are limited to:
- Host the dependency container.
- Wire the business logic implementations into the container.
- Set up asset bundles for JS and CSS.
- Host WebAPI services.
- Enforce security, perform logging and diagnostics.
- Interfacing with application caches for performance.
Another great thing about an SPA is it can increase bandwidth of your team. One group can blast out the services while the other lays in the client app. Since you can easily stub or mock REST services, you could have a fully working client app on mock services and swap out for the real ones when they're done.
You do have to invest up front on Angular, but it pays off big. Since you are already familiar with MVC, you have a leg-up on some of the core concepts.