What is the radius in degrees of your circumpolar region be for Dallas Texas?

To calculate your circumpolar region you need your latitude.

Circumpolar Region Radius Degrees = 90 - Degrees Latitude

If you are in Dallas Texas, your latitude is approximately 32.78 degrees North.

Your circumpolar region radius degrees = 90 - 32.78 = 57.22 degrees.

This means that all stars within 57.22 degrees of the North Celestial Pole will never set below your horizon.