From the record
“State Highway 29 Bridge at the Colorado River is located in both Burnet and Llano counties in the U.S. state of Texas, between Buchanan Dam and Inks Lake. It is also known as Inks Lake Bridge, and was added to the National Register of Historic Places listings in both counties on October 10, 1996.”
Wikipedia article State Highway 29 Bridge at the Colorado River, CC BY-SA 4.0.
One of 6 National Register listings published here for Burnet County · listed in 1996 · category: Structure.
Sources: the Wikipedia article · the case file at the National Archives · the National Register database, National Park Service

