In order to back up their judgments about art, art critics need to have which of these?

The correct answer is: A strong knowledge of art history

Explanation:

Art critics, in order to analyse and judge any piece of art, must have a strong knowledge of art history. This is required for various reasons; first of all, in order to make an analysis, they need to know what they are talking about; and secondly, they need to make comparisons to similar works, so they need the knowledge to do that.