Question

At 6 o’clock the angle formed between the hands of a clock is
A. Straight angle
B. Right angle
C. Acute angle
D. Obtuse angle

Answer 1

Hint: This problem deals with finding the angle between the chosen sectors. We know that a clock has 12 hour stands, though a day has 24 hours, but we can only see 12 hours on the clock. There is only one hour hand, one minute hand and one second hand in any clock. If it is any x o’clock, then the hour hand is on the x hour stand, whereas the minute hand is on the 12 hour stand.

Complete step-by-step solution:
Given that the time on the clock is 6 o’clock.
Which means that the hour hand is on 6, and minute hand is on 12.
Visualizing the information as given below:

We can see that in the above picture the hour hand is on 6, whereas the minute hand is on 12.
As we know that in the clock there are 12 hour stands.
A circle has an angle ${360^ \circ }$, at the center.
As the hour stands divide the clock into 12 slices or 12 pies or 12 sectors.
The angle taken by each sector is given by:
$ \Rightarrow \dfrac{{{{360}^ \circ }}}{{12}} = {30^ \circ }$
Thus each sector takes ${30^ \circ }$.
The angle taken by each sector is = ${30^ \circ }$
Now when the time is 6 o’clock, there are six sectors between the minute hand and the hour hand.
The number of sectors between the minute hand and the hour hand is = 6
$\therefore $The angle associated with the five sectors is given by the product of five sectors and the angle for each sector, as given below:
$ \Rightarrow 6 \times {30^ \circ }$
$ \Rightarrow {180^ \circ }$
$\therefore $The angle between the minute hand and the hour hand at 6 o’clock is ${180^ \circ }$, which is a straight angle.
The angle between the hands of the clock, at 6 o’clock is ${180^ \circ }$, is a straight angle.

Option A is the correct answer.

Note: Please note that while finding the angle between the minute hand and the hour hand at 6 o’clock, there is a chance of confusion, whether to consider the angle in the clockwise direction angle between the minute and the hour hand, or the anti-clock wise direction angle. The anti-clock wise direction angle between the minute hand and the hour hand is also a straight angle i.e, ${180^ \circ }$. Hence either of the ways give the same final answer.