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

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Best answer

Given, 

ABCD is a quadrilateral

∠C +∠D = k ∠AOB 

∵∠D +∠C = k 

= ∠A +∠B = 360°- k 

= ∠OAB +∠OBA =  \(\frac{360°-k}{2}\)

= 360°- \(\frac{360°-k}{2}\)

\(\frac{k}{2}\) = k = 2

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