Question

At what angle are the hands of a clock inclined at \(15\) minutes past \(5\)?

• A. \(73\dfrac{1}{2}^\circ\)
• B. \(67\dfrac{1}{2}^\circ\)
• C. \(59\dfrac{1}{2}^\circ\)
• D. \(65^\circ\)

Hint:

For clock angle problems: \[ \theta = \left| \frac{11M}{2} - 30H \right| \] Always take the absolute value to ensure the angle is positive.

Answer 1

The Correct Option is B

Concept: The angle between the hour hand and minute hand is calculated using: \[ \theta = \left| \frac{11M}{2} - 30H \right| \] where:

• \(H\) = hour
• \(M\) = minutes

Step 1: Write the given time. Time: \[ 5:15 \] Thus, \[ H = 5,\quad M = 15 \]

Step 2: Substitute into the formula. \[ \theta = \left| \frac{11\times15}{2} - 30\times5 \right| \] \[ = \left| \frac{165}{2} - 150 \right| \] \[ = \left| 82.5 - 150 \right| \] \[ = 67.5^\circ \]

Step 3: Express in mixed fraction form. \[ 67.5^\circ = 67\dfrac{1}{2}^\circ \] Hence, \[ \boxed{67\dfrac{1}{2}^\circ} \]