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Knowing the angle between the hour hand and the minute hand, how to solve this kind of math problem? There'd better be an example ... I'm in a hurry and want a high score from an expert!
Because it takes 60 minutes for the minute hand to walk around! A circle is 360 degrees.

So the minute hand walks 6 degrees every minute.

Similarly, the hour hand goes 1/2 degrees per minute.

At 1, the angle between the minute hand and the hour hand is 30 degrees.

At 1: 50.

The minute hand went 6*50.

Clockwise clock has gone (1/2)*50.

So the angle between the hour hand and the minute hand is: (6*50)-( 1/2)*50-30=225 degrees.

In the same way; In a similar way

At 2 o'clock, the angle between the minute hand and the hour hand is 60 degrees.

So at 2 o'clock, 18,

The angle between the hour hand and the minute hand is (6 *18)-(1/2) *18-60 = 39 degrees.

At 7: 35, the minute hand just reached the 7 o'clock position.

So we just need to count how many degrees the hour hand has gone, which is the reading of the angle between the minute hand and the hour hand at 7: 35.

35*( 1/2)= 17.5 degrees

At 5: 30, the minute hand reached the position where the pointer was at 6 o'clock.

Clockwise clock goes 60 minutes from 5 o'clock to 6 o'clock, which means it goes 30 degrees.

5: 30, 15 degrees.

So the angle between the minute hand and the hour hand is 30- 15= 15 degrees.

The latter two can also be calculated like the first two, but it is very simple to calculate like what.