The Angle Between the Minute and Hour Hands of a Clock at 8:30 is

Question:

The angle between the minute and hour hands of a clock at 8:30 is

(a) \(80^\circ\)

(b) \(75^\circ\)

(c) \(60^\circ\)

(d) \(105^\circ\)

Solution

At \(8:30\),

Minute hand position:

\[ 30 \times 6^\circ = 180^\circ \]

Hour hand position:

\[ 8 \times 30^\circ + 30 \times \frac{1}{2}^\circ \]

\[ = 240^\circ + 15^\circ \]

\[ = 255^\circ \]

Required angle:

\[ |255^\circ – 180^\circ| \]

\[ = 75^\circ \]

Hence, the correct option is:

(b) \(75^\circ\)