Beginner object rotation question

I can’t seem to figure out how to rotate this object in the way I want to. I want to snap it so it lays flat on the face below it while keeping the edges snapped together where the cursor is. I need to keep the edges flush.

Looking at the grid in the background you are not align to any axis so you may select the edge of your object and add a custom transform orientation (the plus sign next to global, local, normal, …) make the rotate gizmo visible and rotate your object.