When the temperature increases while the amount of moisture in the air stays the same, the relative humidity decreases. This is because warmer air can hold more moisture than cooler air.
In your scenario, if the temperature rises from 90° F to 100° F, and if the relative humidity remains constant at 80%, then the absolute humidity (the actual amount of water vapor in the air) would not change, but the capacity of warmer air to hold moisture increases.
As a result, the relative humidity would actually drop when the temperature increases from 90° F to 100° F.
So, the correct answer is: The relative humidity drops.