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# Clock Angle Formula

Clocks are used to tell the time of the day. The clock is provided with three hands to measure time which are an hour hand, minute hand, and second hand. A clock has a total of 12 divisions of a total measure of angle 360^{o}. The clock angle formula is used to calculate the time between any two hands of the clock. The clock angle formula is explained below with solved examples.

## What Is the Clock Angle Formula?

Before learning the clock angle formula, let us understand a few things about a clock. There are 12 divisions in a clock. The angle between any two divisions is 30^{o}. Each division is further divided into 5 equal parts and each part equals 1 minute and has an angular distance of 6^{o}. A list of parts and their corresponding angles are given below.

Minutes |
Angular Value |

1 minute | 6^{o} |

2 minutes | 12^{o} |

3 minutes | 18^{o} |

4 minutes | 24^{o} |

5 minutes | 30^{o} |

6 minutes | 36^{o} |

7 minutes | 42^{o} |

8 minutes | 48^{o} |

9 minutes | 54^{o} |

10 minutes | 60^{o} |

Let us see the applications of the clock angle formula in the following section.

## Example on Clock Angle Formula

**Example 1: **Find the clockwise angle between the hour hand and minute hand at 3:30 P.M.(assume the hour hand is fixed at 3 for this hour).

**Solution**

To find: Angle between the hour hand and minute hand

Divisions between the hour hand and minute hand at 3:30 P.M. is 3.

Using the clock angle formula,

The angle between any two divisions is 30^{o}.

Therefore, the angle will be 3 × 30^{o} = 90^{o}

**Answer: The angle between the hour hand and minute hand at 3:30 P.M. is 90 ^{o}.**

**Example 2: **Find the clockwise angle between the minute hand and the hour hand at 12:55 A.M (assume the hour hand is fixed at 12 for this hour).

**Solution**

To find: Angle between the hour hand and minute hand

Divisions between the hour hand and minute hand at 12:55 P.M. is 11.

Using the clock angle formula,

The angle between any two divisions is 30^{o}.

Therefore, the angle will be 11 × 30^{o} = 330^{o}

**Answer: The angle between the hour hand and minute hand at 12:55 P.M. is 330 ^{o}.**

**Example 3: **If a clock shows 4:00 PM then what is the measure of the angle made between an hour hand and a minute hand.

**Solution**

To find: Angle between the hour hand and minute hand.

At 4:00 PM the minute hand of the clock is on the number 12 and the hour hand is on the 4. The angle formed is 4× 30^{o} = 120^{o}

**Answer: The angle between the hour hand and minute hand at 4:00 P.M. is 120 ^{o}.**

## FAQs on Clock Angle Formula

### What Is the Use of Clock Angle Formula?

The clock angle formula is used to determine the measure of the angle formed between an hour hand and a minute hand.

### What Value Does a Clock Angle Formula Give When the Clock Shows 12 Hours?

According to clock angle formula theory at 12 hours the measure between the hour hand and the minute hand is 360^{o}.

### What Value Does a Clock Angle Formula Give When the Clock Shows 1 Hour?

According to clock angle formula theory at 1 hour the measure of the clockwise angle formed between the hour hand and the minute hand is 30^{o}

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