Diagonal $B D$ of parallelogram $A B C D$ forms angles of $45^{\circ}$ with side $B C$ and the height drawn from vertex $D$ to side $A B$.

Find angle $A C D$.

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From the condition, it follows that the specified height is parallel to side $B C$, therefore, this height coincides with side $D A$, which means $A B C D$ is a rectangle (see figure). Since $\angle A B D = \angle C B D = 45^{\circ}$, $B D$ is the bisector of angle $B$ of this rectangle, hence $A B C D$ is a square. Consequently, $C A$ is the bisector of angle $C$ of the square, which means $\angle A C D = 45^{\circ}$.

![](https://cdn.mathpix.com/cropped/2024_05_06_34fd2032e75750f56a92g-08.jpg?height=286&width=323&top_left_y=0&top_left_x=879)

## Answer

$45^{\circ}$.