Notes
three congruent rectangles iv solution

Solution to the Three Congruent Rectangles IV Puzzle

Solution by Symmetry

Rotating the diagram by $90^\circ$ fills in the fourth rectangle. Drawing in the diagonal of the lower left rectangle thereby creates an isosceles triangle. As it is formed by the diagonals of two congruent rectangles that are at right-angles to each other, these diagonals are also at right-angles. Therefore the isosceles triangle is a right-angled triangle and so its angles are $45^\circ-45^\circ-90^\circ$. The angle is therefore $45^\circ$.