[ Rectangular triangles (other). ]
[Concurrency of heights. Angles between heights.]

A line perpendicular to the hypotenuse $A B$ of a right triangle $A B C$ intersects the lines $A C$ and $B C$ at points $E$ and $D$ respectively.

Find the angle between the lines $A D$ and $B E$.
Consider triangle $A B D$ (see figure). From the condition, it follows that lines $A C$ and $D E$ contain its altitudes, that is, $E$ is the orthocenter of this triangle. Therefore, line $B E$ contains the third altitude of the triangle, that is, $B E \perp A D$.

# Answer

$90^{\circ}$.

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