From the given options, at what angle are the hands of a clock inclined at 10 minutes to 2 (smaller angle)?

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Accepted Answer

At **10 minutes to 2**, the positions of the clock hands are as follows:

#### Step 1: Minute Hand Position
- The minute hand is at the **10th-minute mark**.
- Each minute represents **6°** (since $$360^\circ \div 60 = 6^\circ$$).
- The angle of the minute hand from the **12 o'clock position** is:  
  $$
  	ext{Minute hand position} = 10 	imes 6 = 60^\circ.
  $$

#### Step 2: Hour Hand Position
- The hour hand moves **30° per hour** ($$360^\circ \div 12 = 30^\circ$$) and **0.5° per minute** ($$30^\circ \div 60 = 0.5^\circ$$).
- At **1:50 (10 minutes to 2)**, the hour hand is slightly ahead of the **2-hour mark**:  
  $$
  	ext{Hour hand position} = (1 	imes 30) + (50 	imes 0.5) = 30 + 25 = 55^\circ.
  $$

#### Step 3: Angle Between Hands
The angle between the hour and minute hands is:  
$$
	ext{Angle} = |	ext{Minute hand position} - 	ext{Hour hand position}| = |60 - 55| = 65^\circ.
$$

#### Step 4: Smaller Angle
Since this angle is less than $$180^\circ$$, it is already the smaller angle.

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Thus, the smaller angle between the clock hands at **10 minutes to 2** is **65°**, making Option **2** correct.

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