Find x in the fourth circle.

The angle formed by two intersecting chords is half the sum of the measures of the intercepted arcs. The angle 20 degrees intercepts an arc. The angle x intercepts another arc. The sum of the arcs is 215 degrees. The angle formed by the two chords is 20 degrees. The intercepted arcs are x and 215 degrees. Therefore, 20 = (x + 215) / 2. Multiplying by 2, we get 40 = x + 215. Subtracting 215, we get x = 40 - 215 = -175. This result is not possible for an angle. Re-examining the image, the 20 degree angle is an inscribed angle. The arc intercepted by the 20 degree angle is 20 * 2 = 40 degrees. The arc of 215 degrees is given. The angle x intercepts the remaining arc. The total arc is 360 degrees. The arc intercepted by x is 360 - 215 - 40 = 105 degrees. Therefore, x = 105 / 2 = 52.5 degrees.

x = 52.5°