【Solution】Solution: According to the problem, we know:
From the first coincidence to the second coincidence, the minute hand rotates one more circle than the hour hand. The distance difference is $9-1=8$ circles, the catch-up time is: $1 \div 8=\frac{1}{8}, \frac{1}{8} \times 360=45^{\circ}$. Therefore, the answer is: 45
10. (5 points) As shown in the figure, it is a toy clock. When the hour hand makes one complete revolution, the minute hand makes 9 revolutions. If the two hands overlap at the beginning, then when the two hands overlap again, the degree the hour hand has turned is $\qquad$ .

