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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.

Submit your solution

Please do send in your solution to this problem to  weeklymaths@kcl.ac.uk  You can scan or photograph your written work, or type your solutions. If this is your first weekly maths challenge solution, please include your year group and the name of the school you attend. We'll be happy to provide you with feedback on your solution.

 

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