If the bisectors of two adjacent angles \( A \) and \( B \) of a quadrilateral \( A B C D \) int...

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If the bisectors of two adjacent angles \( A \) and \( B \) of a quadrilateral \( A B C D \) intersect at a point \( O \), such that \( \angle C+\angle D=k \angle A O B \), then find the value of \( k \).
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