5. Each of the diagonals of the inscribed quadrilateral $A B C D$ is the bisector of one of the angles from which it is drawn, and also divides the second angle in the ratio $1: 3$. What can the angle $\angle A$ of this quadrilateral be? Express the answer in degrees. List all possible options. If necessary, round the answer to the hundredths or write it as a common fraction.
Answer: $108,72,60,120$.