Question

The smaller angle between the hour and minute hands in a clock when the time is 7:16 am (in degrees) is

• A. \(122^\circ\)
• B. \(136^\circ\)
• C. \(138^\circ\)
• D. \(124^\circ\)

Hint:

For clock angle problems, directly use \(\theta=\left|30H-\frac{11M}{2}\right|\) for faster calculation.

Answer 1

The Correct Option is A

Concept: Angle between hour hand and minute hand: \[ \theta=\left|30H-\frac{11M}{2}\right| \] where: \[ H=\text{hour},\; M=\text{minutes} \]

Step 1: Substitute the given time.
Given: \[ H=7,\;M=16 \] \[ \theta=\left|30(7)-\frac{11(16)}{2}\right| \] \[ =\left|210-\frac{176}{2}\right| \] \[ =\left|210-88\right| \] \[ =122^\circ \]

Step 2: Check smaller angle.
Since: \[ 122^\circ < 180^\circ \] It is already the smaller angle. Thus, the required angle is: \[ \boxed{122^\circ} \]