Look at my answer to this question. Instead of using the user name and password, your backend could provide an additional resource that allows the user to create a token with a special scope.
In your AngularJS application you can use the $http or $resource services (if the ngResource module is included) and obtain such kind of token that allows you to access only the parts of your backend your client really needs.
This token must be cached at the client side and included in the header of each request.
In AngularJS storing the token in the header of each request can be done at a central place if you are using the config function of the module you created.
app.config(function($httpProvider) { $httpProvider.defaults.xsrfCookieName = "TOKEN" }
AngularJS also provides some additional security features. For example you could use the JSON vulnerability protection mechanism. If you are using this, your backend had to add the characters )]}', (you could also override the default characters) to each JSON response body.
For other clients the JSON response will be invalid Javascript code, but in your AngularJS application the characters will be automatically removed.
UPDATE
The best way for implementing security for your application would be reading and understanding the OAuth2 specification.
In this video from minute 11:36 to 17:26 the JavaScript flow is described.
This site provides some implementation of the standard for different programming languages.
Some of the aspects in this standard are that all clients and redirect urls must be registered in an additional authentication server. Client are identified by a unique client id.
To avoid that some other application intercepts your requests for extracting the token, the original token should only be active for a small amount of time and each api request must be SSL encrypted.
For providing Single sign-on also refresh tokens can be used.