Notes
three congruent rectangles v solutions

Solution to the Three Congruent Rectangles V Puzzle

Solution by Angles in an Isosceles Right-Angled Triangle

With the points labelled as above, line segments $A E$ and $E D$ are diagonals of congruent rectangles, so are of equal length. The two rectangles are at right-angles to each other, so angle $A \hat{E} D$ is $90^\circ$. Hence triangle $A E D$ is an isosceles right-angled triangle so angle $E \hat{D} A$ is $45^\circ$.