An angle is inscribed in the circle as shown.

C. 55

The angle is half of the arc of the circle it cuts in the case 110/2= 55

You can prove this to yourself by knowing that all the circle arcs will always add to the full 360 of a circle, and then that the interior 3 angles of a triangle will always add to 180

So for this case 110+150+100=360
Becomes 55+75+50=180 for the triangle that would be created by the initial angle x