A) work out the value of X and give a reason for your answer. b) work out the value of y and give a reason for your answer.

a). x = 106°

b). y = 127°

Step-by-step explanation:

a). Since, "angle subtended by an arc at the center is twice the angle subtended at the circumference"

  x° = 2(53°)

  x = 106°

b). Since, "Opposite angles of a cyclic quadrilateral are supplementary angles"

  Therefore, y° + 53° = 180°

   y = 180°- 53°

   y = 127°

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Step-by-step explanation:

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