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1.
Exiting a US interstate highway at any point to access the service road or feeder street.
On the way to the Whataburger, I needed to pee but had missed the last off ramp, so I took a Texas exit to get to the gas station. -or- When I was telling Billy how to get to my house, instead of waiting for the next off ramp, he immediately made a Texas exit.
by TomKas July 18, 2008
 
2.
When you're jammed in traffic in the state of Texas and you've had enough of not moving, sitting in the Texas sun sweating like a jackass, you drive off the side of the interstate at a 45 degree angle through the ditch in your pickup truck.
This traffic is B.S.! Let's pull a Texas Exit.
by GGAustin August 11, 2011