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 5 of 5: Conclusion
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36∘\boxed{36^\circ}
Detailed analysis

The regular pentagon attains the bound, hence the maximum possible minimum angle is 36∘36^\circ.