Question

When it is 10:30, what kind of angle is formed by the hands of the clock?
A. Acute
B. Obtuse
C. Right
D. Straight

Answer 1

Hint: For solving this question, we first need to find out the angle any two consecutive numbers in clock make. Using this we will calculate the angle between the minute hand and hour hand of the clock. Since time is 10:30, so the minute hand will be at 6 and hour hand will be between 10 and 11. At last, from the formed angle we will determine the type of angle.

Complete step-by-step answer:
Here the angle between any two consecutive numbers in a clock is ${30}^{\circ }$.
Now we know that when time is 30 minutes, then the minute clock will be at 6.
And when time is 10:30, the hour clock will be between 10 and 11. Let us draw a clock here for better understanding.

Now the number of parts (number) between 6 to 10 are 4. So an angle between 6 and 10 will be $4\times {30}^{\circ }={120}^{\circ }$. Similarly, there are 5 parts between 6 to 11. So the angle between 6 and 11 will be $5\times {30}^{\circ }={150}^{\circ }$.
Hence our angle will be between ${120}^{\circ }\text{ and }{150}^{\circ }$ and it will be exactly in middle of 10 and 11, so angle will be equal to ${\displaystyle \frac{{120}^{\circ }+{150}^{\circ }}{2}}={\displaystyle \frac{{270}^{\circ }}{2}}={135}^{\circ }$.
Hence our required angle between the hands of a clock as 10:30 is ${135}^{\circ }$.
Since ${135}^{\circ }$ is greater than ${90}^{\circ }$ so it is an obtuse angle.

So, the correct answer is “Option B”.

Note: Students can also directly see from the diagram that angle between 6 and 9 would be ${90}^{\circ }$ so any angle greater than that would be obtuse. Here, we have taken exactly half of 10 and 11, because the minute hand was at exactly half of the full circle (30 minutes out of 60 minutes).