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Problem 619

AIME late

Geometry Difficulty 5.1 Find the answer

9. (6 points) As shown in the figure, the clock displays $9: 15$ , at this time the angle between the minute hand and the hour hand is $\qquad$ degrees.

Your answer

Official solution

【Answer】Solution: According to the analysis, calculate clockwise:
$\begin{array}{l} 3 \times 30=90 \text { (degrees), } \\ (6-0.5) \times 15 \\ =5.5 \times 15 \\ =82.5 \text { (degrees), } \\ 90+82.5=172.5 \text { (degrees); } \end{array}$

Answer: At 9:15, the angle between the minute hand and the hour hand is 172.5 degrees. Therefore, the answer is: 172.5.

Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic, difficulty and ordering added by this site.