# Solution to the Angle Formed by Three Rectangles Puzzle +-- {.image} [[AngleFormedbyThreeRectangles.png:pic]] > Three congruent rectangles. What’s the angle? =-- ## Solution by [[Triangles]] +-- {.image} [[AngleFormedbyThreeRectanglesLabelled.png:pic]] =-- With the points labelled as in the diagram above, the [[line segments]] $A D$, $D F$, and $F A$ all have the same length since they are diagonals of [[congruent]] rectangles. This means that triangle $A D F$ is an [[equilateral triangle]] and so angle $A \hat{F} D$ is $60^\circ$. In triangle $D F I$, angle $D \hat{I} F$ is $90^\circ$ and sides $I D$ and $I F$ have the same length. Therefore, triangle $D F I$ is an [[isosceles]] [[right-angled triangle]] so angle $I \hat{F} D$ is $45^\circ$. Putting these together, angle $A \hat{F} B = 60^\circ - 45^\circ = 15^\circ$. This is the same as angle $K \hat{F} D$ and so angle $I \hat{F} K$ is $45^\circ - 15^\circ = 30^\circ$. Therefore, angle $E \hat{F} G = 360^\circ - 90^\circ - 90^\circ - 30^\circ = 150^\circ$.