Yes, it is very much possible to use typescript in an Angular JS application. You will have to install the typings for Angular. You can do this with the TypeScript Definition Manager. Basically what this does is tell typescript how Angular is (strict) typed.
npm install -g tsd
tsd install angular
AngularJS is an undisputed champion among all the front end web development frameworks, well I am no expert to say that since honestly I have not worked much with other popular libraries like Knockout, backbone, amberJS etc. but for last few months I have been exploring the AngularJS and I am loving it.
AngularJS brings several goodies to the table, it's very well designed, robust and well thought framework. In my opinion if you are a web developer, it’s totally worth it to invest your time learning angularJS even if you do not work much on the front end and do not plan to use it in your project in near future.