APMO 2011 Problem 2

Five points $A_1,A_2,A_3,A_4,A_5$ lie on a plane in such a way that no three among them lie on a same straight line. Determine the maximum possible value that the minimum value for the angles $\angle A_iA_jA_k$ can take where $i, j, k$ are distinct integers between $1$ and $5$ .