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Weather | Natural Extremes | Air Quality | Environmental Watch. Rye is located in east Texas. Rye is part of Liberty County. On average, the public school district that covers Rye is worse than the state average in quality. The Rye area code is 281.
Dawson County, Texas. Dawson County is a county in the U.S. state of Texas. As of the 2010 census, its population was 13,833.[1] The county seat is Lamesa.[2] The county was created in 1876 and later organized in 1905.[3] It is named for Nicholas Mosby Dawson,[4] a soldier of the Texas Revolution.