Here's another approach:
Draw a 3rd line from the center to the bottom point of tangency (where the triangle side touches the circle).
This divides the circle into 3 equal sectors (pieces of pie).
360/3 = 120, so each sector has an angle of 120 degrees at the center.
So, the unlabeled angle in the diagram = 120 degrees, which makes angle x = 240 degrees.