When sin x = -0.866= (sqrt3)/2, basic angle of x = 60 degrees. Since sin x is negative, x is in 3rd and 4th quadrant, hence x is 180+60=240, 360-60=300.
Given cos x is -0.5, basic angle is 60 degrees. Since cos is negative, x is located in 2nd and 3rd quadrant, 180-60=120, 180+60=240.
Therefore, the anwser that satisfies both equations are 240 degrees.