You need to use the axis-lock feature of your protractor or rotation tool. If you orient the tool to the desired axis first (for instance, by pointing it toward the appropriate horizon or other plane), you can lock that orientation by holding down the shift key while moving the tool to your desired object. Then click the point that you want as the origin of rotation.
Here’s a discussion of a similar problem: Orient a circle to a plane but placed on a different plane - #5 by DanYHKim