Confirmed with photo evidence! The bike lane on South 2nd Street runs from South Glebe Road to South Irving Street. Continuing east from there along South 2nd Street, you will continue to have sharrows until reaching South Courthouse Rd.
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Western end of the bike lane at South Glebe Road/South 2nd St
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Eastern end of the bike lane at South Irving St/South 2nd St
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Map of the area
The painting isn’t finished as the bicycle symbols and crosswalks have not been painted, but the changes so far are appreciated. This still leaves a block and a half gap between Irving and Highland where there are no markings, but hopefully the county can add sharrows at 2nd/Irving for cyclists traveling east.