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Challenge 239: Quadrilateral Quandary

Three of the angles in a cyclic quadrilateral are xo, kxo and mxo, where k and m are positive integers.

If the largest angle in the quadrilateral is 160o, how many possible pairs of values k and m are there, and what are they?

Hint: you might like to start by trying some small values of k and m to see how it works.

Justify your answer carefully.

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