In a quadrilateral ABCD, inscribed in a circle, angle ABD = 52, angle ADC = 84, find the angle B of the quadrilateral.

To solve the problem, consider the figure.

By the property of the angles of a quadrangle inscribed in a circle, in any quadrangle inscribed in a circle, the sum of opposite angles is 180.

Therefore, ∠ ABC + ∠ ADC = 180.

∠ ABC = 180 – 84 = 96.

Answer: The value of the angle ABC = 96.

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