It depends on what degree of longitude you assign the two points, as the shoreline at Myrtle Beach runs steeply NE-SW, and at Nags Head NW-SE, so even a small difference in longitude can make a mile or two difference in latitude between the two points. That said, as identified in Google Earth I get a figure of 189 statute or 164 nautical miles at the longitude of Myrtle Beach. Measuring at the longitude of Nags Head the distance is approximately 183 statute miles or 159 nautical miles. SO, it depends, and without the question specifying which degree of longitude is to be used there is no true answer!!!! Measurements were rounded to the closest even mile in both cases.