\( A B C D \) is a quadrilateral in which the bisectors of \( \angle A \) and \( \angle C \) mee...

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\( A B C D \) is a quadrilateral in which the bisectors of \( \angle A \) and \( \angle C \) meet \( D C \) produced at \( Y \) and \( B A \) produced at \( X \), respectively. Prove that \( \angle X+\angle Y=\frac{1}{2}(\angle A+\angle C) \).
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