Question

Through how many degrees does the hour hand of a clock turn from $4:00$ pm to \[8:00\] pm of the same day?

Answer 1

Hint:Consider the twelve hour clock system here. Divide the clock into twelve sections of each hour, and then find the angle covered in each section as the whole clock is a circle and have a whole angle of ${360^0}$. Then keeping the reference as 12’o o'clock, find the angle at $4:00$ pm and then find the angle at \[8:00\] pm and then subtract to get the required angle in degrees.

Complete step by step solution:
To find out how many degrees does the hour hand of a clock turn from $4:00$ pm to \[8:00\] pm of the same day, we will first consider this question is based on the twelve hour clock system. Now we know that in a complete cycle a clock turns ${360^0}$ and also a clock has twelve sections of one hour each.
So let us find angle of turn for one hour
$ = \dfrac{{{{360}^0}}}{{12}} = {30^0}$
Now finding angle of turn when clock is at $4:00$ pm, taking reference as 0’o clock or 12’o clock,
$4 - 0 = 4$ so there are four sections in between them
$\therefore $ angle of turn $ = 4 \times {30^0} = {120^0}$
Similarly for \[8:00\] pm,
Angle of turn $ = (8 - 0) \times {30^0} = 8 \times {30^0} = {240^0}$
Now subtracting them to get the required degrees,
${240^0} - {120^0} = {120^0}$
$\therefore {120^0}$ is the required answer.

Note: You can directly find the answer to this question by product of angle of turn for one section/hour and sections/hours present between $4:00$ pm to \[8:00\] pm.
In this question, it is given that to find degrees for the same day, but let us consider it as asked for after $n$ days then you have to add $360n$ to the answer.