I have setup Webstorm to recognise and compile my coffeescript files.
I have installed the AngularJS plugin and can successfully write my controllers etc in plain o
To fix the specific problem Unresolved variable or type angular
you need to make sure the angular javascript libraries have been Enabled
(see image below).
You do this via the WebStorm settings:
File -> Settings -> Javascript -> Libraries
Here is the relevant help section: Configuring JavaScript Libraries
In WebStorm v.11
Profit
Settings screenshot
With webstorm 10 you are going to go to the preferences window and from there select Languages & Frameworks > JavaScript > Libraries. Then click the download button, select TypeScript community stubs from the dropdown at the top of the list, find angular and click download and install.
If you are using jshint be sure to go to the jshint settings find the Predefined option and add angular:true to suppress warnings.