At which time do the hands of an analog clock form an interior right angle?

Rationale

At 9:00, the hands of an analog clock form an interior right angle.

At this time, the hour hand points directly at the 9, and the minute hand points at the 12, creating a perfect 90-degree angle between them.

A (2:35) YOUR ANSWER

At 2:35, the minute hand is on the 7, and the hour hand is slightly past the 2. The angle formed between the hour hand and the minute hand is not a right angle but rather an obtuse angle, as it exceeds 90 degrees.

B (3:15) YOUR ANSWER

At 3:15, the minute hand points at the 3 and the hour hand is a quarter of the way between the 3 and 4. This configuration results in an angle that is also not a right angle, since it is less than 90 degrees.

D (6:00) YOUR ANSWER

At 6:00, the hour hand is on the 6 and the minute hand is on the 12, forming a straight line rather than an angle. Thus, the hands are not forming a right angle at this time, as they are instead aligned in a 180-degree configuration.

Conclusion

The only time among the choices when the hands of an analog clock form a right angle is at 9:00, where the hour and minute hands are positioned to create a 90-degree angle. The other options either result in acute or obtuse angles, or in the case of 6:00, a straight angle. Understanding the positions of the clock hands at various times is crucial for determining angular relationships.

At which time do the hands of an analog clock form an interior right angle?

At 9:00, the hands of an analog clock form an interior right angle.

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