is the centre of the circle.  BC  is chord of the circle and  A  is point on the circle. If  ∠BAC  =  x,   ∠OBC  =  y , then  x + y  is

The question seems to be incomplete. The center of the circle is not specified. However, if we assume that O is the center of the circle, then by the properties of a circle, the angle subtended by a chord at the center is twice the angle subtended by it at any point on the alternate segment.

So, ∠BAC = x and ∠BOC = 2x (since O is the center and BC is the chord)

Given that ∠OBC = y, and in triangle BOC, the sum of angles is 180 degrees, we have ∠BOC + ∠OBC + ∠BCO = 180

Substituting the given values, we get 2x + y + ∠BCO = 180

To find the value of x + y, we need the value of ∠BCO, which is not provided in the question. If additional information is provided, we can solve for x + y.