Question

Draw hands of a clock when they make an angle ${{30}^{\circ }}$.

Answer 1

Hint: We solve this question by first finding the angle between each number in the clock and then we see how many parts of 12 can be used to get that angle. Then we can find all the possibilities of the hands of a clock making ${{30}^{\circ }}$ and draw them.

Complete step-by-step answer:
A clock is in the form of a circle. As the angle in a circle is ${{360}^{\circ }}$, the total angle of a clock is ${{360}^{\circ }}$.
A clock has 12 hours, that is a clock is divided into 12 parts. So, the angle ${{360}^{\circ }}$ is divided into 12 parts.
Then angle between each part is,
$\dfrac{{{360}^{\circ }}}{12}={{30}^{\circ }}$
So, the angle between each part is ${{30}^{\circ }}$.
Now, we need to draw the hands of a clock when they make an angle ${{30}^{\circ }}$.
A general clock looks as below.

As angle between each part is equal to ${{30}^{\circ }}$, when the hands of the clock are adjacent to each other then the angle between them is ${{30}^{\circ }}$.

So, angles between the hands of the clock are ${{30}^{\circ }}$ when the hands of the clock are on any of the above lines adjacent to each other.

So, by changing the hands from one part to another but keeping them adjacent to each other and then interchanging between hours hand and minutes hand we can form many diagrams with an angle ${{30}^{\circ }}$.

Note: The common mistake one makes while solving this question is taking the complete angle of the circle as ${{180}^{\circ }}$. Then dividing the angle into 12 parts we get angle between each part as ${{15}^{\circ }}$. So, to make ${{30}^{\circ }}$ we need to take two parts as one part. Then all such parts possible are the answer. But it is wrong as the angle of the circle is ${{360}^{\circ }}$.