2. The clock shows half past eight. What is the angle between the hour and minute hands?
Answer: $75^{\circ}$.

Solution. At the moment when the clock shows half past eight, the minute hand points to the number 6, and the hour hand points to the midpoint of the arc between the numbers 8 and 9 (see figure). If two rays are drawn from the center of the clock to the adjacent 

![](https://cdn.mathpix.com/cropped/2024_05_06_0b5079389ba7141ce391g-07.jpg?height=277&width=257&top_left_y=818&top_left_x=1688)

6 numbers on the clock face, the angle between them is $360^{\circ} \div 12 = 30^{\circ}$. The angle between the clock hands when they show half past eight is two and a half times larger. Therefore, it is $75^{\circ}$.