At 17 1, (1) 1: 20, what is the angle between the hour hand and the minute hand? What is the angle between the hour hand and the minute hand at 2: 00? (2) From 1: 05 to 1: 35, how far did the minute hand and the hour hand turn? (3) How many degrees should the minute hand of the clock rotate clockwise from 4 o'clock to coincide with the hour hand? Test center: clock face angle. Analysis: draw a sketch and solve it by using the characteristics of the clock plate. Solution: (1)∫ Minute hand goes per minute 1 grid, and hour hand goes per minute ∴ 1.20 minutes. The angle between the hour hand and the minute hand is [20-(5+)] The angle between the hour hand and the minute hand is [15-(10+× 20) ]×××15 ]× grid, = 80, = 22.5. (2) From 1 to 15 to 65438. The rotation angle of the minute hand is (35- 15)× the rotation angle of the hour hand is × 120 = 120. (3) Assuming that the minute hand needs to rotate clockwise by X degrees to coincide with the hour hand, then the hour hand rotates clockwise. It can only coincide with the hour hand. X = 120, x degrees, ∴ the minute hand rotates clockwise (130 172). The minute hand and the hour hand on the clock are like two athletes running around the runway day and night. Please answer the question about the clock: (1) Minutes per minute. (2) A few minutes after noon 12, the obtuse angle formed by the minute hand and the hour hand will be equal to 12 1? (3) After the obtuse angle formed by the minute hand and the hour hand in (2) is equal to 12 1, the obtuse angle formed by the two needles is equal to 12 1 for the second time after a few minutes. Test center: clock face angle. Analysis: (1) The clock dial is divided into 12 squares, and each square is divided into 5 squares, so the dial * * * is divided into 60 squares, and the diagonal degree of each square is 6 degrees. The minute hand turns a square every minute, and the angle of 6 degrees is 1 minute; (2) The obtuse angle formed by the minute hand and the hour hand is equal to 12 1, which can be set as x minutes, and then it can be solved according to the above equidistant relationship equation. (3) The obtuse angle formed by two hands will be equal to 12 1 for the second time, that is, 360- 1265438. (2) The rotation degree of the hour hand per minute is 360÷(60× 12)=0.5 (degrees). Let the obtuse angle formed by the minute hand and the hour hand be 12 1 degree for the first time after x minutes, then (6-0.5) x = 10. (3) Let the obtuse angle formed by the minute hand and the hour hand be 12 1 degree for the second time and 12 1 degree for the second time after y minutes, that is, 360- 12 1=239 (degree When designing a rectangular clock face, an extracurricular study group wants to make the width of the rectangle 20 cm, the center of the clock is at the intersection of the diagonal lines of the rectangle, the number 2 is at the vertex of the rectangle, and the numbers 3, 6, 9, 12 are at the midpoint of the side, as shown in the figure. (1) When the hour hand points to the number 2, what is the angle between the hour hand and the minute hand? (2) Please point out the position of the number 1 on the long box and explain the method of determining the position; (3) Please point out the positions of the remaining numbers on the clock face in the long box and write the corresponding numbers (note: draw the necessary auxiliary lines to reflect the idea of solving problems); (4) What should be the length of the rectangle? Test center: clock face angle. Analysis: draw a picture and solve it by using the characteristics of the clock plate. Solution: Solution: (1) The included angle between the hour hand and the minute hand is 2× 30 = 60; (2) As shown in the figure, let the intersection of the diagonal lines of the rectangle be O, and the corresponding points of the numbers 12 and 2 in the rectangle are A and B respectively, connecting OA and OB. Method 1: Make the bisector of ∠AOB, and AB crosses at point C, then point C is the position of the number 1. Method 2: Set the number 65438+. Tan30 = positioning number1; , so (3) as shown in the figure; (4)∵OA= 10，∠AOB=60，∠OAB=90，tan60 = ∴AB=OA？ Tan 60 = 10 ∴ The length of this rectangle is centimeters. Comments: This question examines the angle between the hour hand and the minute hand of a clock. In the clock problem, the degree relationship between the rotation of the hour hand and the minute hand is often used: every time the minute hand rotates 1, the hour hand rotates () degrees, and the angle graph is established by using the position relationship between the hour hand and the minute hand at the starting time. Answer: WD. Examination questions: teacher py 168. ★ As shown in the figure, the next day, Teacher Wei asked the students two questions: (1) If you put 0.5 kg of vegetables on the scale, how many angles did the pointer turn? (2) If the pointer turns to 540, how many kilograms are these dishes? Test center: clock face angle. Analysis: (1) Calculate the rotation angle of 1 kg of vegetables on the scale and multiply it by 0.5; (2) Let 540 be divided by 1 kg of rotation angle of vegetables. Solution: (1), 0.5× 18 = 9, put 0.5 kg of vegetables on the scale and turn the pointer 9; (2)540÷ 18=30 ((kg)), A: * * * There are 3 kg of vegetables. Comments: The key to solve this problem is to get the rotation angle of 1 kg vegetables on the scale. Answer: Teacher Lan Chong; Exam: Miss Liu Lina. ☆ ☆ ☆ ☆ ☆ ☆ ☆ ☆ ☆ ☆ ☆ ☆ ☆ ☆ ☆ ☆ ☆ ☆ ☆ ☆ ☆ ☆ ☆ ☆ ☆ 97 Analysis: (1) If the hour hand moves from 2: 30 to 2: 55, * * 25 minutes later, the hour hand turns 30 degrees in 60 minutes, 1 minute turns 0.5 degrees, the minute hand turns 360 degrees, and 1 minute turns 6 degrees, answer accordingly; (2) At 2 o'clock, the hour hand points to 2, after 15 minutes, the rotation angle is 15× 0.5 = 7.5, 2 o'clock, the minute hand points to 3, and the included angle with 2 is 30. Then the degree of acute angle formed by hour hand and minute hand is 30-7.5 = 22.5. Solution: (1) minute hand angle: (360 ÷ 60) × (55-30) = 150, hour hand angle: () (2) (360 ÷12)-/kloc-0. ☆ ☆ ☆ ☆ ☆ ☆ ☆ ☆ ☆ ☆ ☆ ☆ ☆ ☆ ☆ ☆ ☆ ☆ ☆ ☆ ☆ ☆ ☆ ☆ ☆ 97 Analysis: According to the meaning of the question, suppose Li Gang went home and left X, then he left in minutes (2× 1 10+x), and the degree of the hour hand can be obtained. Because the hour hand runs 30 hours, we can find out the time it takes Li Gang to go out. Solution: Set the hour hand to walk home from Li Gang. Then minutes passed (2× 1 10+X), and from the meaning of the question, it was found that x = 20, because the hour hand walked 30 per hour, which was an hour, that is, it took Li Gang 40 minutes to go out. Comments: This question examines the angle between the hour hand and the minute hand. In the clock problem, the hour hand and the minute hand are often used to rotate. Examination: py 168 teacher. ☆☆☆☆☆☆☆☆☆☆☆☆☆☆☆☆☆☆☆☆☆☆☆☆☆☆☆☆☆973 Solution: 9: 20, the difference between the hour hand and the minute hand is 5 squares. The included angle between every two adjacent numbers is 30 degrees, = 160. At 9: 20, the angle between the minute hand and the hour hand is 5× 30. Comments: The knowledge points used are: 12 number on the clock, and the included angle between every two adjacent numbers is 30. Answer: Mr. Huang Ling. Hidden analytical experience training to collect opinions. (2) Between 10: 30 a.m. and 1 1: 30 a.m., when does the hour hand and the minute hand form a right angle? Test center: clock face angle. Analysis: draw a picture and solve it by using the characteristics of the clock plate. Solution: (1) As shown in the figure, the scale on the clock divides a circle into 12 equal parts, each part is 30, and the angle between the hour hand and the minute hand on the clock face is 4.5. (2) The hour hand turns 30 degrees in 60 minutes, 0.5 degrees in one minute, 360 degrees in the minute hand and 6 degrees in one minute. It can be assumed that x minutes pass from 10: 30 in the morning, and the hour hand and the minute hand are at right angles. The equation is: 135-6x+0.5x=90. Find the solution. At 1 1, the angle between the hour hand and the minute hand is 30 degrees. Suppose that in another y minutes, the angle between the hour hand and the minute hand is a right angle. According to the meaning of the question, 30+6y-0.5y=90, and the solution is y= 10 169. In the following statement, the correct number is three. ② At six o'clock on the clock, the angle formed by the hour hand and the minute hand is a right angle; ③ At twelve o'clock on the clock, the angle formed by the hour hand and the minute hand is rounded; (4) the clock on the clock-at 6: 15, the angle formed by the hour hand and the minute hand is a right angle; At nine o'clock on the clock, the angle formed by the hour hand and the minute hand is a right-angle test center: the clock face angle. Analysis: draw a picture and solve it by using the characteristics of the clock. Solution: Solution: ① At 9: 15 on the clock, the angle formed by the hour hand and the minute hand is 180-30÷ 4, not a right angle, wrong; ② At six o'clock, the hour hand points to 6, and the minute hand points to 12, forming a right angle, which is correct; ③ At twelve o'clock on the clock, both the hour hand and the minute hand point to 12, and the angle formed is rounded, which is correct; (4) The clock is off-at six o'clock, the angle formed by the hour hand and the minute hand is 90+30, not a right angle, which is wrong; ÷⑤At nine o'clock, the hour hand points to 9 and the minute hand points to 12, forming a right angle, which is correct. The correct number is three. Comments: This question examines the calculation of the rotation angle of the clock minute hand. In the clock problem, the degree relationship between the rotation of the hour hand and the minute hand is often used: every time the minute hand rotates 1, the hour hand rotates. Exam: Teacher Zhang CF. Hidden analysis experience training collection comments download exam basket 170 students, have you seen the alarm clock? Its hour hand and minute hand are like two brothers racing, but do you know how many degrees the hour hand goes every minute? How many degrees does the minute hand go? When you figure this out, you can solve many interesting problems about alarm clocks: (1) The angle between the hour hand and the minute hand is 90 degrees at 3 o'clock sharp; (2) The included angle between the hour hand and the minute hand is 72.5 degrees at 7: 25; (3) How many times are the hours and minutes perpendicular to each other during the day and night (0:00-24:00)? Test center: clock face angle. Analysis: (1) See that there are several big squares between the hour hand and the minute hand, and one big square represents 30; (2) The method is the same as (1); (3) When the hour hand is perpendicular to the minute hand, the included angle is 90. First get the number of minutes that can be vertical once, and then look at the number of minutes that can be obtained in 24 hours. Solution: (1) 3× 30 = 90; (2)2 ×30 =72.5 ; (3) Let x minutes pass from one vertical to the next, then 6x-0.5x=2×90 5.5x= 180 Solution: (1) The minute hand rotation degree is 360÷60=6 (degrees); (2) The rotation degree of the hour hand per minute is 360÷(60× 12)=0.5 (degrees). Let the obtuse angle formed by the minute hand and the hour hand be 12 1 degree for the first time after x minutes, then (6-0.5) x = 10. (3) Let the obtuse angle formed by the minute hand and the hour hand be 12 1 degree for the second time and 12 1 degree for the second time, that is, 360- 12 1=239 (degree). On the basis of 12 1 degree, that is, 239-121=18 (degree), then (6-0.5) y =/kloc-0. It is found that the obtuse angle formed by two hands will be equal to 12 1 for the second time within y= (minutes). Therefore, after the obtuse angle formed by the minute hand and the hour hand is equal to 12 1, it will be commented that this question examines the characteristics related to the angle of the clock dial. The clock dial is divided into 12 squares, so each dial * * * is divided into 60 squares, and the diagonal degree of each square is 6. The minute hand turns once every 60 minutes, and the hour hand turns 1, that is, the minute hand turns 360, and the hour hand turns 30, that is, the minute hand turns1the hour hand turns 30.