2. At a certain moment, Anna measured the angle between the hour and minute hands of her clock. Exactly one hour later, she measured the angle between the hands again. The angle turned out to be the same. What could this angle be? (Consider all cases).

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# Solution:

After 1 hour, the minute hand remains in its place. During this time, the hour hand has turned $30^{\circ}$. Since the angle has not changed, the minute hand must be dividing one of the
![](https://cdn.mathpix.com/cropped/2024_05_06_aa3023726f3a3c515454g-2.jpg?height=436&width=902&top_left_y=1606&top_left_x=452)

angles between the positions of the hour hand (additional angle in $\left.330^{\circ}\right)$.

This means that either the hour hand was at $15^{\circ}$ earlier, or $165^{\circ}$ later.

Answer: $15^{\circ}$ or $165^{\circ}$.