APMO 2011 - Asian Pacific Mathematics Olympiad Question 2

Five points $A_1,A_2,A_3,A_4,A_5$ lie in a plane with no three collinear. Determine the maximum possible value of the minimum of the angles $\angle A_iA_jA_k$, where $i,j,k$ are distinct integers between 1 and 5.

Illustrative configuration (new):