The angle between the minute hand and the hour hand of a clock when the time is 4.20, is

### Concept & Angle Between Clock Hands The angle $\theta$ between the hour and minute hands of a clock at $H$ hours and $M$ minutes can be found using the standard absolute difference formula: $$\theta = \left| 30H - 5.5M \right|$$ ### Step-by-Step Solution 1. **Given:** The time is 4:20. Here, the hour component $H = 4$ and the minute component $M = 20$. 2. Apply the clock angle formula: $$\theta = \left| 30(4) - 5.5(20) \right|$$ 3. Calculate the hour term: $30 \times 4 = 120°$ 4. Calculate the minute term: $5.5 \times 20 = 110°$ 5. Find the absolute difference: $$\theta = |120° - 110°| = 10°$$ ### Exam Strategy & Shortcut Using logical visualization: At 4:20, the minute hand is exactly on the 4. The hour hand has moved past the 4 for exactly 20 minutes. The hour hand moves at $0.5^\circ$ per minute. Since it moved for 20 minutes, it shifted $20 \times 0.5^\circ = 10^\circ$ away from the 4. The distance between the hands is exactly $10^\circ$. ### Common Pitfall A common mistake is assuming both hands are perfectly aligned on the 4 at 4:20, leading students to incorrectly choose 0°. You must account for the continuous movement of the hour hand. ### Final Answer Therefore, the correct answer is **10°**.