In your open map view, select Window > ArcToolbox. A 3rd window, occupied by the elements of ArcToolbox, appears on the left. Select ArcToolbox > Data Management Tools > Projections and Transformations > Define Projection (dbl-click on the latter):
A Define Projection window appears (below left):
Select the folder button for input dataset (red arrow above left), scroll to your
*_county_LL folder (above right); select county_roads.shp; press Add The Define Projection window returns (below) with the county_roads shapefile and a default “assumed” coordinate system, which needs to be changed to Geographic, NAD 1983:
Select the button on the RH side of the “Coordinate System” window (red arrow above).