How can I tell whether a (Drupal 7) web app was built using Angular by looking at the page source, and not having to ask the developers?
If it's an online site you can use http://builtwith.com/ and it usually can give you a good and useful bunch of information about that site.
However if they are using angular you can take a look at their page sources to see if they are using any attributes of angular like ng-repeat for example
You can also take a look at the sources that your browser get while browsing that site to see if javascript files for angularjs are included among the sources.