Answers

2016-01-12T22:58:29+05:30
see figure
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proof
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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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