In cyclic quadrilateral ABCD, if \(\angle A = 70^{\circ}\) and \(\angle B = 80^{\circ}\), find \(\angle D\).
100°
In any cyclic quadrilateral, opposite angles are supplementary (they add up to \(180^{\circ}\)), because each pair of opposite angles subtends the full circle from opposite arcs.
In the given figure, vertices A and B are adjacent at the base, with C and D at the top, so the opposite pairs are (A, C) and (B, D).
Since \(\angle B\) and \(\angle D\) are opposite, \(\angle D = 180^{\circ} - \angle B = 180^{\circ} - 80^{\circ} = 100^{\circ}\).
Hence, \(\angle D = 100^{\circ}\).
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