A tire pressure monitoring apparatus, for mounting on a vehicle wheel that is configured to have a tire mounted thereon and that has a first opening, includes a tire monitor for sensing pressure in the tire. The tire monitor includes a housing having a spherical surface and a second opening that extends through the spherical surface. A tire valve stem is configured to extend through the first and second openings, and the valve stem has a threaded portion. The apparatus further includes a threaded fastener that is engageable with the threaded portion of the valve stem for attaching together the tire monitor and the valve stem. The fastener has a spherical surface that is engageable with the spherical surface of the housing when the fastener is engaged with the threaded portion of the valve stem.