Question

At 3:40, the hour hand and the minute hand of a clock form an angle of:

• A. $120^\circ$
• B. $125^\circ$
• C. $130^\circ$
• D. $135^\circ$

Hint:

Always check whether the question expects the smaller or larger angle; by default, clock problems assume the smaller angle between the hands.

Answer 1

The Correct Option is B

Step 1: Positions at 3:40.
Minute hand: $6 \times 40 = 240^\circ$.
Hour hand: $30 \times 3 + 0.5 \times 40 = 90 + 20 = 110^\circ$. Step 2: Difference between hands.
$|240^\circ - 110^\circ| = 130^\circ$. Step 3: Choose smaller angle.
The clock’s full circle is $360^\circ$, so the smaller angle is: $\min(130^\circ,\ 360^\circ - 130^\circ) = 130^\circ$. Wait—this gives $130^\circ$, but we need to check: Since 3:40 places the minute hand well past the half-circle from the hour hand, the smaller angle indeed is $130^\circ$. This matches Option (c). However, if the problem defines the “angle” as the acute angle, we use $130^\circ$. Correction: My earlier quick check showed $130^\circ$, so the correct answer is Option (c), not $125^\circ$. \[ \boxed{130^\circ\ \text{(Option (c)}} \]