From 2 o'clock to 4 o'clock, how many times did the hour hand of the clock and the minute hand form an angle of 60 degrees? What are the time and minutes?

From 2 o'clock to 4 o'clock, how many times did the hour hand of the clock and the minute hand form an angle of 60 degrees? What are the time and minutes?

Four times, 2:00, 2:20, 3:05, 3:25

(1) When does the minute hand and the hour hand coincide between three and four? (2) the hour hand and the minute hand coincide at two thirty
(1) Between three o'clock and four o'clock, when does the minute hand and the hour hand on the clock return? When is the right angle? When is the straight line? (2) what is the angle between the hour hand and the minute hand at 2:30?
Equation of one degree with one variable! Up to 15 points can be added!

1) The speed of the hour hand is 30 / 60 = 1 / 2
Minute hand 60 minutes walk 360 ° minute hand speed = 360 / 60 = 6
At 3 o'clock, the hour hand points to 3, the minute hand points to 12, and the difference between them is 90 degrees
It can be seen as a problem of pursuit (the minute hand pursues the hour hand). When the minute hand pursues the hour hand, it coincides
90 ÷ (6-1 / 2) = 180 / 11 = 16 and 4 / 11 (min)
That is, at 3:16 and 4 / 11, the minute hands and the hour hands coincide
(90 + 90) / (6-1 / 2) = 360 / 11 = 32 and 8 / 11 (points)
That is, at 3:32 and 8 / 11, the minute hand and the hour hand form a right angle
(90 + 180) / (6-1 / 2) = 540 / 11 = 49 and 1 / 11 (min)
That is, at 3:49 and 1 / 11, the minute hand and the hour hand form a straight line
2) At 2:30, the minute hand goes 180 ° from 12 to 30, with time = 180 △ 6 = 30 (min)
At the same time, the clock moves 1 / 2 × 30 = 15 degrees
At this time, the angle between the hour hand and minute hand is 180 ° - 60 ° - 15 ° = 105 °

When the clock is 4:15, how many degrees is the angle between the hour hand and the minute hand

Because a dial is 360 ° and has 12 divisions, each dial is 30 ° so it is 120 ° at 4 o'clock, and then the minute hand is 15 minutes, which is 1 / 4 of the hour hand. Therefore, when the hour hand moves 30 ° further, it is 7.5 ° so the degree of the hour hand is 127.5 ° and then minus 90 ° of the minute hand, which is 37.5 °