A) Built an API B) Used an MVC Framework (front or back end)
This can be easily overcome by following either a book like "AngularJS in Action" or spending some time using a framework on a small scale project.
At the end of the day, I've found that when using Angular, my code is much easier to read, maintain, and reason about. I used it for one project about a year ago, and just started another project with it last week - which was easy since I'd spent some time with it previously.
Never feel that you should be intimidated by a technology; but definitely be able to reason about its use cases and the value it may add to your toolbox.
I stuck with Angular because I tend to write larger applications, and Angular had shining recommendations from those using it in similar contexts.