Stage: 3 Challenge Level: 
If you know the sizes of the angles marked with coloured dots in this diagram which angles can you find by calculation? Explain your reasoning. Draw some diagrams of your own and mark in these angles. If in addition you know that the lines $AB$ and $CD$ are parallel which angles can you find?
Creating expressions/formulae. Combinatorics. Mixed triangles. Number - generally. Generalising. Visualising. Pythagoras' theorem. Small software. Mathematical reasoning & proof. Number theory.
Published May 2000.
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