## Challenge 239: Quadrilateral Quandary

Three of the angles in a cyclic quadrilateral are *x*^{o}, *kx ^{o} *and

*mx*

^{o}, where

*k*and

*m*are positive integers.

If the largest angle in the quadrilateral is 160^{o}, 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.