What's the angle between the hour hand and the clock?

What's the angle between the hour hand and the clock?

At 1:20,
The angle between minute hand and 12 o'clock direction is 30 * 4 = 120 degrees
The angle between the clockwise and 12 o'clock is 30 + 30 * 20 / 60 = 40 degrees
Included angle: 120-40 = 80 degrees
At 2:15,
The angle between minute hand and 12 o'clock direction is 30 * 3 = 90 degrees
The angle between the clockwise and 12 o'clock is 30 * 2 + 30 * 15 / 60 = 67.5 degrees
Included angle: 90-67.5 = 22.5 degrees

What is the angle between the minute hand of the clock and the hour hand (less than 180 °) at 8:28?

At 8 o'clock, the angle between minute hand and hour hand is 180 + 60 = 240 degrees,
Because the minute hand moves 6 ° per minute, and the hour hand moves 0.5 ° per minute
So in 28 minutes, the minute hand walked 28 × 6 = 168 ° and the hour hand walked 0.5 × 28 = 14 ° respectively
So at 8:28, the angle between the minute hand of the clock and the hour hand is 240 + 14-168 = 86 degrees