Answer

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**Hint:**As we know that the hour hand of the clock makes ${360^ \circ }$in 12 hours. So, in 1 hour, the hour hand moves ${30^ \circ }$. Now we divide this by 60 minutes and we get the degrees of hour hand made in 1 minute. Then we calculate the minutes at 4.24 pm. Now we multiply the degrees of hour hand made in 1 minute and minutes at 4.24 pm.

**Complete step-by-step answer:**

According to the question we have to find the degree of hour hand made at 4.24 pm

As we know that in 12 hours a clock made angle = ${360^ \circ }$

Now the angle made by the hour hand of the clock in 1 hour = $\dfrac{{{{360}^ \circ }}}{{12}}$

\[ = {30^ \circ }\]

So, the angle made by the hour hand of the clock in 1 minute= $\dfrac{{30}}{{60}}$

$ = {\dfrac{1}{2}^ \circ } = {0.5^ \circ }$

As we know that 1 hour = 60 minutes

Now we calculate the total number of minutes from 12.00 to 4.24 pm we get

$ = 4 \times 60 + 24$

$ = 240 + 24$

$ = 264$

Therefore the total number of minutes=264 minutes

Now we calculate the angle made by clock in 264 minutes we get

$ = 264 \times \dfrac{1}{2}$

$ = {132^ \circ }$

The angle made by the hour hand of the clock at 4.24 pm is ${132^ \circ }$

**So, the correct answer is “Option C”.**

**Note:**For solving these type of questions we have to always remember that the angle made by the hour hand is ${360^ \circ }$. Therefore we divide it by 12 hours, this gives us the angle made by the clock per hour i.e. \[{30^ \circ }\].Lastly calculate the total number minutes made by the hour hand for a given time.

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