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2014-12-25T22:35:50+05:30

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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


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