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 1 of 5: Lower-bound construction
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36∘36^\circ
Detailed analysis

Five vertices of a regular pentagon have every angle formed by three vertices at least 36∘36^\circ, so the optimum is at least 36∘36^\circ.