A quadrilateral inscribed in a circle has one angle measuring 120 degrees and an ad...
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Problem
A quadrilateral inscribed in a circle has one angle measuring 120 degrees and an adjacent angle measuring x degrees. Find x.
Step-by-step solution
In a cyclic quadrilateral, opposite angles are supplementary. Therefore, $x + \angle C = 180^{\circ}$ and $\angle A + \angle C = 180^{\circ}$. Given $\angle C = 120^{\circ}$, we have $x + 120^{\circ} = 180^{\circ}$.
Answer
$60^{\circ}$