Another interesting problem!
Suppose you have a quadrilateral ABCD where AB is parallel to CD and such that the length of DA = AB = BC and BD = DC.
What are the angles of this quadrilateral?
Hint: Obviously, a trigonometry solution is possible with some work. But there’s another way, without writing down a single number! Keep in mind your shapes and rules about certain, specific edges being equal to one another as in this problem.