Question

When the clock shows time 5:20, the angle formed between the two hands is
(a) Obtuse
(b) Right
(c) Acute
(d) None of these

Answer 1

Hint: We will draw a rough sketch to see how the clock looks at the time indicating 5:20. Then we will look at the types of angles and their definitions. After that, we will see the diagram and identify the type of angle made by the two hands of the clock. This will lead us to the desired answer.

Complete step by step solution:
The time shown on the clock is 5:20. So, the hour hand should be on 5 and the minute hand should show that 20 minutes have passed. We know that there are 12 intervals on the clock and each interval marks the passing of 5 minutes using the minute hand. So, for the minute hand to show that 20 minutes have passed, it should point to the fourth interval. We will draw a rough diagram to display the positions of the two hands of the clock as follows,

We know that the angle is called an acute angle when it is less than $90{}^\circ $ and it is called an obtuse angle when it is greater than $90{}^\circ $. If the angle is equal to $90{}^\circ $, then it is called a right angle. From the figure, we can see that the hour hand is pointing at 5 and the minute hand is pointing at 4. The angle between the two hands appears to be less than $90{}^\circ $. Hence, we can conclude that the angle formed by the two hands while indicating the time 5:20 is an acute angle.
The correct option is (c).

Note: In this type of question, it is always useful to draw a rough diagram to understand the given information. We should be familiar with the types of angles and their definitions. The way in which the time is denoted is an important part of this question. There are different formats with which we can denote at the same time. So, we should pay close attention to such information to avoid making any mistakes.