A clock is started at noon. By 10 minutes past 5, the hour hand has turned through

### Concept & Hour Hand Speed The hour hand rotates 360° in 12 hours. Therefore, it moves: - $30°$ per hour. - $0.5°$ (or $1/2°$) per minute. ### Step-by-Step Solution 1. **Given:** Start time = 12:00 Noon. End time = 5:10 PM ("10 minutes past 5"). 2. Calculate the total time elapsed: Time = 5 hours and 10 minutes. 3. Convert this total time entirely into minutes: $$5 \text{ hours} = 5 \times 60 = 300 \text{ minutes}$$ Total = $300 + 10 = 310 \text{ minutes}$. 4. Multiply the total minutes by the hour hand's speed (0.5°/min): $$\text{Angle} = 310 \times 0.5° = 155°$$ ### Exam Strategy & Shortcut Calculate hours and minutes separately: 5 hours = $5 \times 30° = 150°$ 10 minutes = $10 \times 0.5° = 5°$ Total angle = $150° + 5° = 155°$. This is much faster for mental math! ### Common Pitfall A common error is just calculating for the 5 hours (150°) and ignoring the extra distance the hour hand creeps forward during the additional 10 minutes. ### Final Answer Therefore, the correct answer is **155°**.