The angle just above 40 degrees angle = 1/2 * 70 = 35 making the 'double' angle at top = 35 + 40 = 75. The 'double' angle opposite = 180 - 75 = 105 ( because opposite angles of a cyclic quadrilateral add up to 180 degrees). Also the top angle of this one = 40 degrees ( because 2 equal sides both subtend same angle).
So the bottom angle = 105-40 = 65 degrees.
Now x = this angle ( alternate segment theorem )
Therefore x = 65 degrees.