Q. If a clock shows 9:15, what is the angle between the hour and minute hands?
A.
112.5 degrees
B.
90 degrees
C.
135 degrees
D.
75 degrees
Solution
At 9:15, the hour hand is at 97.5 degrees (9*30 + 15*0.5) and the minute hand is at 90 degrees (15*6). The angle between them is |97.5 - 90| = 7.5 degrees.
Q. If it is 2:30, what is the angle between the hour and minute hands?
A.
105 degrees
B.
120 degrees
C.
135 degrees
D.
150 degrees
Solution
At 2:30, the hour hand is at 75 degrees (2*30 + 30*0.5) and the minute hand is at 180 degrees (30*6). The angle between them is |75 - 180| = 105 degrees.
Q. If the minute hand is at 12 and the hour hand is at 4, what is the angle between them?
A.
120 degrees
B.
90 degrees
C.
60 degrees
D.
150 degrees
Solution
At 4:00, the hour hand is at 120 degrees (4 hours * 30 degrees) and the minute hand is at 0 degrees. The angle between them is |120 - 0| = 120 degrees.
Q. If the time is 1:50, what is the angle between the hour and minute hands?
A.
130 degrees
B.
140 degrees
C.
150 degrees
D.
160 degrees
Solution
At 1:50, the hour hand is at 95 degrees (1 hour * 30 degrees + 50 minutes * 0.5 degrees) and the minute hand is at 300 degrees (50 minutes * 6 degrees). The angle between them is |95 - 300| = 205 degrees.
Q. If the time is 2:30, what is the angle between the hour and minute hand?
A.
105 degrees
B.
120 degrees
C.
135 degrees
D.
150 degrees
Solution
At 2:30, the hour hand is at 75 degrees (2 hours * 30 degrees + 30 minutes * 0.5 degrees) and the minute hand is at 180 degrees (30 minutes * 6 degrees). The angle between them is |75 - 180| = 105 degrees.
Q. If the time is 2:30, what is the angle between the hour and minute hands?
A.
105 degrees
B.
120 degrees
C.
135 degrees
D.
150 degrees
Solution
At 2:30, the hour hand is at 75 degrees (2 hours * 30 degrees + 30 minutes * 0.5 degrees) and the minute hand is at 180 degrees (30 minutes * 6 degrees). The angle between them is |75 - 180| = 105 degrees.
Q. What is the angle between the hour and minute hand at 12:30?
A.
165 degrees
B.
180 degrees
C.
150 degrees
D.
135 degrees
Solution
At 12:30, the hour hand is at 165 degrees (12 hours * 30 degrees + 30 minutes * 0.5 degrees) and the minute hand is at 180 degrees (30 minutes * 6 degrees). The angle between them is |165 - 180| = 15 degrees.
Q. What is the angle between the hour and minute hand at 12:45?
A.
135 degrees
B.
150 degrees
C.
165 degrees
D.
180 degrees
Solution
At 12:45, the hour hand is at 337.5 degrees (12 hours * 30 degrees + 45 minutes * 0.5 degrees) and the minute hand is at 270 degrees (45 minutes * 6 degrees). The angle between them is |337.5 - 270| = 67.5 degrees.
Q. What is the angle between the hour and minute hand at 5:25?
A.
135 degrees
B.
150 degrees
C.
165 degrees
D.
180 degrees
Solution
At 5:25, the hour hand is at 162.5 degrees (5 hours * 30 degrees + 25 minutes * 0.5 degrees) and the minute hand is at 150 degrees (25 minutes * 6 degrees). The angle between them is |162.5 - 150| = 12.5 degrees.
Q. What is the angle between the hour and minute hands at 12:45?
A.
135 degrees
B.
150 degrees
C.
165 degrees
D.
180 degrees
Solution
At 12:45, the hour hand is at 337.5 degrees (12 hours * 30 degrees + 45 minutes * 0.5 degrees) and the minute hand is at 270 degrees (45 minutes * 6 degrees). The angle between them is |337.5 - 270| = 67.5 degrees.
Q. What is the angle between the hour and minute hands at 5:25?
A.
120 degrees
B.
130 degrees
C.
140 degrees
D.
150 degrees
Solution
At 5:25, the hour hand is at 162.5 degrees (5 hours * 30 degrees + 25 minutes * 0.5 degrees) and the minute hand is at 150 degrees (25 minutes * 6 degrees). The angle between them is |162.5 - 150| = 12.5 degrees.
Q. What is the angle between the hour hand and the minute hand at 12:30?
A.
165 degrees
B.
180 degrees
C.
150 degrees
D.
120 degrees
Solution
At 12:30, the hour hand is at 165 degrees (12*30 + 30*0.5) and the minute hand is at 180 degrees (30*6). The angle between them is |165 - 180| = 15 degrees.
