# Clock Aptitude Reasoning Tricks & Problems - Finding Angle Between The Hands of a Clock Given Time

TLDRThe video script provides a detailed explanation of how to calculate the angle between the hour and minute hands of an analog clock at various times. It begins with a step-by-step guide for the time 12:30, illustrating the process of determining the position of both hands and the angles involved. The script then extends the method to other times, such as 12:00 and 10:25, using fractions to represent the hour hand's position between two numbers. It also covers the calculation of both the shortest and longest angles between the hands. The explanation includes visual aids like drawings and emphasizes the importance of understanding the relationship between hours, minutes, and degrees in a full circle.

###### Takeaways

- π The angle between the minute and hour hands on a clock can be calculated based on the time shown.
- π Each hour on the clock represents an angle of 30 degrees, as a full circle is 360 degrees and there are 12 hours.
- β± At 12:30, the minute hand is at 6 and the hour hand is halfway between 12 and 1, creating an angle of 165 degrees between the hands.
- π’ To find the angle for a specific time, determine the fraction of the hour that has passed and calculate the corresponding angle in degrees.
- π For times like 1:20, the hour hand is one-third of the way from 1 to 2, which translates to an angle of 20 degrees from the 1 o'clock position.
- π The total angle between the hands at 1:20 is 80 degrees, obtained by adding the angles between the hour numbers and the fractions of the hour.
- π At 11:15, the minute hand is at 3 and the hour hand is one-fourth of the way from 11 to 12, resulting in an angle of 112.5 degrees between the hands.
- π For the time 10:25, the minute hand is at 5 and the hour hand is slightly past 10, with the angle between the hands being 162.5 degrees, the shorter angle.
- π To find the longer angle at 10:25, subtract the shorter angle from 360 degrees, yielding an angle of 197.5 degrees.
- π The shortest angle between the hour and minute hands is always less than 180 degrees, as the hands cannot form a straight line at any given time.

###### Q & A

### At 12:30, what is the position of the minute hand on an analog clock?

-At 12:30, the minute hand, which is the long hand, is pointing directly at the 6 on the clock face.

### How does the position of the hour hand change between 12:00 and 12:30 on an analog clock?

-Between 12:00 and 12:30, the hour hand moves from the 12 towards the 1, but it is exactly halfway between 12 and 1 at 12:30.

### What is the angle between the hour hand and the minute hand at 12:30?

-The angle between the hour hand and the minute hand at 12:30 is 165 degrees.

### How is the angle between the hour hand and the minute hand at 12:30 calculated?

-The calculation involves understanding that each hour represents 30 degrees. At 12:30, the hour hand is halfway between 12 and 1, which is 15 degrees from the 12. Adding the 150 degrees from 12 to 6 gives a total angle of 165 degrees.

### What is the angle between the hour hand and the minute hand at 1:20?

-At 1:20, the minute hand is at 4, and the hour hand is two-thirds of the way between 1 and 2, resulting in an angle of 80 degrees between the two hands.

### How can you determine the position of the hour hand at a given time?

-To determine the position of the hour hand, you can use the minute value divided by 60 to find the fraction of how far it is from one of the hours. The remaining fraction represents the distance from the next hour.

### What is the shortest angle between the hour and minute hands at 10:25 on an analog clock?

-The shortest angle between the hour and minute hands at 10:25 is 162.5 degrees.

### How do you find the shortest angle between the hour and minute hands on an analog clock?

-To find the shortest angle, calculate the angles between the hour and minute hands and the 12 o'clock position, then subtract the smaller angle from 180 degrees or add the smaller angle to the larger one to find the shortest angle.

### What is the angle between the hour hand and the minute hand at 11:15 on an analog clock?

-At 11:15, the angle between the hour hand and the minute hand is 112.5 degrees.

### How can you convert the time on an analog clock to degrees?

-To convert time to degrees, first determine the positions of the hour and minute hands on the clock face, then calculate the angles between these positions using the fact that each hour represents 30 degrees.

###### Outlines

##### π Understanding Clock Angles at 12:30

This paragraph explains how to calculate the angle between the hour and minute hands of an analog clock at 12:30. It starts by establishing that each hour on the clock represents 30 degrees, as the clock completes a 360-degree rotation in 12 hours. At 12:30, the minute hand points at the 6, while the hour hand is halfway between 12 and 1. The calculation involves determining the angle from 1 to 6 (150 degrees) and then finding the half-hour angle (15 degrees) because the hour hand is between 12 and 1. The final angle between the hands is the sum of these, which is 165 degrees. This is a step-by-step guide to understanding the relationship between time and angles on a clock face.

##### π Calculating Clock Angles for 12:00 (120 Degrees)

The second paragraph delves into calculating the angle between the clock hands when the time is represented as 120 degrees, which corresponds to 1:40 on an analog clock. The explanation begins with drawing the clock face and identifying the positions of the hour and minute hands. The hour hand is between 1 and 2, and the minute hand is at the 4, representing 40 minutes past the hour. The calculation involves determining the fraction of the hour that has passed (two-thirds, since 40 minutes is two-thirds of the way to the next hour) and converting this fraction into degrees (20 degrees, which is two-thirds of 30 degrees). The total angle is found by adding the angles between the hour marks (30 degrees each) and the calculated angle, resulting in an 80-degree angle between the hands.

##### π Finding Angles at 11:15 and 10:25

The final paragraph presents methods to find the angles between the clock hands at 11:15 and 10:25. For 11:15, the minute hand is at 3, and the hour hand is between 11 and 12. The calculation uses the fraction of the hour that has passed (one-fourth) to determine the hour hand's position and then calculates the angle as 112.5 degrees. For 10:25, the minute hand is at 5, and the hour hand is between 10 and 11. The calculation involves finding the fraction of the hour passed (five-twelfths) and determining the angles between the hour hand and both 10 and 11. The shorter angle, which is less than 180 degrees, is calculated to be 162.5 degrees. The longer angle can be found by subtracting the shorter angle from 360 degrees, resulting in 197.5 degrees. This paragraph provides a comprehensive approach to solving for clock angles at given times.

###### Mindmap

###### Keywords

##### π‘Analog Clock

##### π‘Minute Hand

##### π‘Hour Hand

##### π‘Angle

##### π‘Degrees

##### π‘12:30

##### π‘Fraction

##### π‘Shortest Angle

##### π‘360 Degrees

##### π‘Example Calculation

###### Highlights

At 12:30, the minute hand is at 6 and the hour hand is between 12 and 1.

The hour hand at 12:30 is exactly in the middle between 12 and 1.

Each hour on the clock represents an angle of 30 degrees.

The angle between the hour hand and minute hand at 12:30 is calculated to be 165 degrees.

For the time 12:00, the angle between the hour and minute hands would be 180 degrees, which is impossible.

To find the angle at 2:40, the hour hand is between 2 and 3, and the minute hand is at 4.

The hour hand at 2:40 is two-thirds of the way from 2 to 3.

The angle between the hour and minute hands at 2:40 is 80 degrees.

At 11:15, the minute hand is at 3 and the hour hand is between 11 and 12.

The hour hand at 11:15 is one-fourth of the way from 11 to 12.

The angle between the hour and minute hands at 11:15 is 112.5 degrees.

For 10:25, the minute hand is at 5 and the hour hand is between 10 and 11.

The hour hand at 10:25 is five-twelfths of the way from 10 to 11.

The shortest angle between the hour and minute hands at 10:25 is 162.5 degrees.

The longer angle at 10:25, if needed, can be found by subtracting the shorter angle from 360 degrees.

All angles on a clock face must add up to 360 degrees.

###### Transcripts

## Browse More Related Video

ANGLES IN A UNIT CIRCLE || PRE-CALCULUS

Converting Radians and Degrees (Precalculus - Trigonometry 4)

Physics 2.4 - Converting Position and Velocity Time Graphs

Speed, Distance, Time - Corbettmaths

Coterminal Angles In Radians & Degrees - Basic Introduction, Trigonometry

How To Find The Reference Angle In Radians and Degrees - Trigonometry

5.0 / 5 (0 votes)

Thanks for rating: