Before 1932: Bethel
In 1935: Proposed Durham - Haddam road
In 1935, the state assigned Route 180 to a proposed trunk line route from Durham to Haddam. The road was never built. I haven't found details, but imagine Route 180 would have extended east from near today's Route 17 / Route 68 intersection in Durham to the Route 81 / Route 154 intersection in Higganum.
If Route 180 were built today, it would form a natural extension of Route 68. The latter route didn't exist in Durham in 1935 when Route 180 was proposed.