
At 5 : 20, the angle formed between the two hands of a clock is
A. Obtuse
B. Right
C. Acute
D. None of these
Answer
520.5k+ views
Hint: We will first try to find the least angle that should be there, by using the fact that each hour contains , so (5 - 4) = 1 contains . Then we will apply the fact that the hour hand advances one full number for each complete rotation of the minute hand through , which means that the minute hand advances 20 minutes or of an hour.
Complete step-by-step answer:
In the question we have been asked to find the angle between the minute hand and the hour hand of the clock if the clock shows 5 : 20 A.M. We know that the angle in a clock is . In a clock the numbers are labelled from 1 to 12 in the perimeter of a circle, thus dividing the clock into 12 sections. So, we can say that if the sections are equally divided, then the angle subtended by each section will be . We also know that in the numbers represented on a clock, every successive section has a difference of 5 minutes between them. So, we can say that for a 5 minutes interval, it contains . So, in one minute, it contains .
In the question, we are given the reading on the clock as 5 : 20, which means that the minute hand is at 4 and the hour hand is slightly past 5, assuming that the hands of the clock rotate relatively smoothly. So, if (5 - 4) is 1, then it will be ( for each hour interval) or will be the least angle between the hands, but the answer is incomplete. Now, we know that the hour hand advances one full number for each hour. So, each hour is represented by a complete rotation of the minute hand through . This means that when the minute hand advance 20 minutes or of an hour, the hour hand also advances by one-third of those or . So, the angle between the hands is . Hence, the angle between the minutes and hour hand of the clock with a reading of 5 : 20 is . And since the angle is less than , it is an acute angle.
Therefore, the correct answer is option C.
Note: There is a formula to solve these kinds of problems in a shortcut method. It is given as , where M means the reading of the minute hand and H means the reading of the hour hand. Since we were not asked the magnitude of the angle, we could have drawn the figure of the clock showing 5 : 20 and then reached a conclusion.
Complete step-by-step answer:
In the question we have been asked to find the angle between the minute hand and the hour hand of the clock if the clock shows 5 : 20 A.M. We know that the angle in a clock is
In the question, we are given the reading on the clock as 5 : 20, which means that the minute hand is at 4 and the hour hand is slightly past 5, assuming that the hands of the clock rotate relatively smoothly. So, if (5 - 4) is 1, then it will be
Therefore, the correct answer is option C.
Note: There is a formula to solve these kinds of problems in a shortcut method. It is given as

Latest Vedantu courses for you
Grade 8 | CBSE | SCHOOL | English
Vedantu 8 CBSE Pro Course - (2025-26)
School Full course for CBSE students
₹45,300 per year
Recently Updated Pages
Master Class 12 Economics: Engaging Questions & Answers for Success

Master Class 12 Maths: Engaging Questions & Answers for Success

Master Class 12 Biology: Engaging Questions & Answers for Success

Master Class 12 Physics: Engaging Questions & Answers for Success

Master Class 12 Business Studies: Engaging Questions & Answers for Success

Master Class 12 English: Engaging Questions & Answers for Success

Trending doubts
What is the Full Form of ISI and RAW

A mixture of sand and water can be separated by the class 9 chemistry CBSE

Latitudinal and Longitudinal extent of India is 30 class 9 social science CBSE

Name the three parallel ranges of the Himalayas Describe class 9 social science CBSE

Which among the following has the highest peak in Eastern class 9 social science CBSE

Who is eligible for RTE class 9 social science CBSE
