It depends on the type of authentication that you have or want to perform to access this API.
The simplest is probably BASIC authentication.
For a BASIC authentication, as per rfc2617, you have to provide a valid BASIC authorization header in your request.
This can be performed by setting this header once for all like this with AngularJS:
$http.defaults.headers.common.Authorization = 'Basic ' + basic-credentials;
Where basic-credentials is the base64 encoded user:password string.
So subsequent requests will use this header and will be authorized by this API.
If you haven't already read it, you can take a look at AngularJS $http documentation which describes how to set HTTP headers and use the $http service.
It also provides an example of BASIC authentication.