MathLabs

Problem 2

Five points A1,A2,A3,A4,A5A_1,A_2,A_3,A_4,A_5 lie in the plane, with no three collinear. Determine the maximum possible value of the minimum angle ∠AiAjAk\angle A_iA_jA_k over all distinct i,j,ki,j,k.
Step 4 of 5: Upper bound
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min⁡∠AiAjAk≤36∘\min\angle A_iA_jA_k\le36^\circ
Detailed analysis

Those two rays and their endpoints form one of the allowed angles, so every configuration has a triple angle at most 36∘36^\circ.