Question

What is the angle between the hour and minute hands when the wall clock shows the time as 8:25?

• A. \(97.5^\circ\)
• B. \(100.0^\circ\)
• C. \(102.5^\circ\)
• D. \(105.0^\circ\)

Hint:

Use the formula: \[ |30H-5.5M| \] where \(H\) is hours and \(M\) is minutes.

Answer 1

The Correct Option is C

Concept: For a clock: \[ \text{Angle moved by hour hand per hour}=30^\circ \] \[ \text{Angle moved by hour hand per minute}=0.5^\circ \] \[ \text{Angle moved by minute hand per minute}=6^\circ \] The required angle is the absolute difference between the positions of the two hands.

Step 1: Find the position of the hour hand. At 8:00, the hour hand is at \[ 8\times30=240^\circ \] In 25 minutes it moves further by \[ 25\times0.5=12.5^\circ \] Hence, \[ \text{Hour hand position}=240+12.5=252.5^\circ \]

Step 2: Find the position of the minute hand. At 25 minutes, \[ 25\times6=150^\circ \]

Step 3: Calculate the angle between the hands. \[ |252.5-150| \] \[ =102.5^\circ \] Therefore, \[ \boxed{102.5^\circ} \]