I would say 'liking' a page is consent to have 'Friend likes this page' appear in your friends' news feeds. It doesn't state that they liked that particular pos

I would say 'liking' a page is consent to have 'Friend likes this page' appear in your friends' news feeds. It doesn't state that they liked that particular post. Annoying or not, I always thought it was reasonably clear that the post was coming from the page, not from the friend.