How can I tell if a Windows 10 PC has the Anniversary Update installed?

Solution 1:

Press WinKey + R, type winver and press ENTER

If the version number reads 1607, then you have the Anniversary Update installed.

Solution 2:

You can determine this by looking at the Start menu, since the Anniversary Update changed it. Before the update, it looked like this (with words):

old style

After the update, it looks like this (just icons):

new style

A particularly salient difference is that the user avatar/name no longer appear at the top; rather, the avatar is above the File Explorer icon.