Question 40

The measure of the smaller angle formed by the hour and minute hand of a clock at 4:00 is 120 degrees.

At 4:00, the hour hand is positioned at 120 degrees, while the minute hand is at 0 degrees. The angle between them is calculated as the absolute difference, which yields 120 degrees.

A) 90 deg

Option A is incorrect because the angle formed at 4:00 is not 90 degrees. At this time, the hour hand is at the 4 mark, which corresponds to 120 degrees, and the minute hand at the 12 mark corresponds to 0 degrees, making the angle between them greater than 90 degrees.

B) 120 deg

Option B is correct as it accurately describes the angle between the hour and minute hands at 4:00. The hour hand at 4 is at 120 degrees, and the minute hand at 12 is at 0 degrees, resulting in an angle of 120 degrees between them.

C) 130 deg

Option C is incorrect because the angle between the hour and minute hands at 4:00 is not 130 degrees. The calculation shows that the actual angle is 120 degrees, which is less than what is indicated in this option.

D) 135 deg

Option D is also incorrect. The measure of the angle at 4:00 is 120 degrees, which is less than 135 degrees. This indicates that the angle between the hour hand and minute hand is not as large as suggested by this option.

Conclusion

The correct answer is 120 degrees, as calculated from the positions of the hour and minute hands at 4:00. Options A, C, and D fail to represent the correct angle, while B accurately reflects the geometry of the clock hands at that time. Understanding the calculation of angles in relation to the positions of clock hands is crucial in determining such measures.