use WordPress Rest API to build a web application

In general, if you want totally headless application, you should not use wordpress but JS, as with JS you will be able to reuse at least some of the code for both server and client sides.

As for using angular theme…. well the question is still why do you use wordpress at all as you will not get any of the benefits of using plugins to enhance the theme, so what is the added value wordpress gives you, an editor? some server side API you are used to work with? That might be a good enough reasons, but the mileage you will get out of wordpress will be considerably less compare to using a proper theme.

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