Clock-Hand Angles

Clock-hand angles: how to solve

1. Identify the two hands. Decide which two clock hands are being compared, then find how far each one has moved from 12 o’clock.

2. Use the clock’s turn structure. A full turn around the clock is 360°, so each hour mark represents 30°.

   • The minute hand moves 6° per minute.
   • The hour hand moves 30° per hour, plus a small extra amount as minutes pass.

3. Find the angle between them. Compute the two hand positions in degrees, then subtract. If needed, take the smaller angle by using the difference from 360°.

4. Simplify the final answer. Give the angle in simplest exact form if the expression is not already a whole number.

Quick check

• The result should be between 0° and 180° if the smaller angle is requested.
• At an exact hour, the hour hand is on a mark and the minute hand is at 12, so the angle should match the number of hour marks between them times 30°.

Helpful strategy

If the time includes minutes, do not place the hour hand exactly on the hour mark. Move it a little forward based on the minutes before calculating the angle.