Fastest way to snap two faces together by aligning their centers in non-standard orientations? In the attached example, I moved the origins of the two shapes to the center of the desired faces.

The objective is to snap the cube's face (where the origin is moved to) to the slanted face. Basically snap origin to origin by aligning the cube to the orientation of slanted face.




Arbitrary orientation
When you have the two objects with the origins in the same location, activate snap vertex option, select the object that needs to rotate and press R, searching for a vertex of the angled face.

If the rotation is not aligned with a view, use custom orientations, and press R followed by the choosen axis twice (i.e. R,X,X will rotate around X local axis).