Angles on a Clock

What this clock-angle puzzle tests

This is a straightforward easy geometry puzzle that asks you to calculate the precise angle between clock hands at a given time. It appears simple on the surface but rewards careful attention to how both hands move continuously as time progresses—not in discrete jumps.

To solve problems like this, you need to track the position of each hand independently. The minute hand moves at a predictable rate based on minutes elapsed; the hour hand moves more slowly and advances gradually between hour markers. The key insight is recognizing that both hands move at constant angular velocities, so you can express their positions as functions of time and find the angle between them.

• Angular velocity of clock hands
• Converting time to angular position
• Finding the acute angle between two rays