All inscribed angles intercepting the same arc have the same measure.
If you slide the vertex of angle y clockwise around the circle until it coincides with the vertex of the angle marked 65°, you see that those two inscribed angles (y and 65°) intercept the same arc, so have the same measure:
y = 65°.
The measure of an inscribed angle is half the measure of the intercepted arc, so the arc marked x is double the angle 65°.
