To find the types of content your audience is interested in, first create a Facebook Profile unconnected to anything. Apparently friends in your list affects your results.
After setting up this account with zero friends, click on the top search bar in facebook, and enter:
1. "Pages liked by people who like [your page]"
2."Interests liked by people who like [your page]"
Posting content your audience is interested in should help in increasing post engagement.