In the figure below, all the small squares on the board are equal. What is the value of the angle $\angle A E F$? Justify.

![](https://cdn.mathpix.com/cropped/2024_05_01_a50b5476db779c3986d5g-31.jpg?height=391&width=343&top_left_y=1901&top_left_x=931)

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Solution

Mark the points $G$ and $H$ as indicated in the figure. The triangles $E F G$ and $A E H$ correspond to half of a $1 \times 3$ rectangle, and consequently $\angle F E G=\angle E A H$ and $\angle E F G=$ $\angle A E H$. Since these triangles are right triangles, we have $\angle E A H+\angle A E H=90^{\circ}$. Thus

$$
\begin{aligned}
\angle A E F & =180^{\circ}-(\angle A E H+\angle F E G) \\
& =180^{\circ}-90^{\circ} \\
& =90^{\circ}
\end{aligned}
$$

![](https://cdn.mathpix.com/cropped/2024_05_01_a50b5476db779c3986d5g-32.jpg?height=383&width=331&top_left_y=826&top_left_x=736)