AB is a chord of the circle. Chord AB makes an angle at the center which is twice the angle it makes at a point on the circumference.
hence w = v = x/2
in the quadrilateral, CGDH,
angle C = y (vertical angle)
sum of angles in the quadrilateral CGDH is
180 - v + y + 180 - w + z = 360
hence, w + v = x = y + z