Question

At 9 O' clock the angle formed between the hands of a clock is
A) Complete angle
B) Reflex angle
C) Zero angle
D) None

Answer 1

Hint:
Here we have to find the angle between the hands of a clock at 9 O'clock. The clock has the shape of a circle and the clock contains the number from 1 to 12. The angle between each consecutive number or each division is \[30^\circ \]. At 9 O'clock, the hour hand points towards 12 and the minute hand points towards 9. We will find the number of divisions between 9 and 12 and then we will multiply it with \[30^\circ \] to get the required angle between the hands of a clock.

Complete step by step solution:
We need to find the angle formed between the hands of a clock at 9’ O clock.
At 9 O'clock, the hour hand points towards 12 and the minute hand points towards 9. Let’s draw the figure for the same.

Case 1: In anticlockwise direction.
The difference between 9 and 12 \[ = 12 - 9 = 3\]
We know the angle between the consecutive numbers or separation between the numbers is \[30^\circ \].
Therefore, the angle between the hands of a clock is equal to the product of their difference and angle between the consecutive numbers.
Required angle between the hands of a clock \[ = 3 \times 30^\circ = 90^\circ \]
Case 2: In clockwise direction:
The actual difference between 9 and 12 \[ = 12 - 3 = 9\]
We know the angle between the consecutive numbers or separation between the numbers is \[30^\circ \].
Therefore, the angle between the hands of a clock is equal to the product of their difference and angle between the consecutive numbers.
Required angle between the hands of a clock \[ = 3 \times 90^\circ = 270^\circ \]
We can observe that the angle between the hands of a clock is a reflex angle is \[90^\circ \] when measured in the anticlockwise direction, which is not given in the option but it is \[270^\circ \] when we measure it in the clockwise direction and it is also known as a reflex angle.

Therefore, the correct option is option B.

Note:
We have seen that the angle between the hands of a clock is a reflex angle. A reflex angle is defined as the larger angle formed i.e. it is more than \[180^\circ \] but it is less than \[360^\circ \]. Here in this question, we have obtained two angles between the hands of a clock, one which is more than \[180^\circ \] is reflex angle and one which is less than \[180^\circ \] is either acute or obtuse angle, but we have got \[90^\circ \], which is known as a right angle.