## What is An Angle?

In geometry, two rays sharing a common endpoint form an angle. The common endpoint is called the vertex, and the two rays are called the arms of the angle.

## Types of Angles

There are three basic types of angles: acute angle, right angle, and obtuse angle.

**Acute angle:** angle measuring less than 90°

**Right angle:** angle measuring exactly 90°

**Obtuse angle:** angle measuring more than 90°

## Definition of An Acute Angle

Any angle that measures greater than 0° and less than 90° is called an acute angle.

∠ABC measures 30° and hence it is an acute angle.

## Examples of Acute Angles

Acute angles measure less than 90°

Therefore, 67°, 45°, 23°, 52°, 86°, 14° are all examples of acute angles.

Dividing the right angle (90˚) will give us two or more acute angles since each newly formed angle will be less than 90˚.

- Right Angle

Right Angle Two acute angles are formed by

dividing the right angle.

## Real – Life Examples of Acute Angles

If we slice a pizza into 5 or more slices, each slice of pizza will make an acute angle.

Each slice of the pizza makes an acute angle.

Another example is the wall clock. The arms of a wall clock make acute angles at several hours of the day. For example, 10 o’clock.

The hour hand and the minute hand form an acute angle at 10 o’clock.

A pair of open scissors, alligator’s open mouth , and the beak of birds all form acute angles.

## Acute Triangle

A triangle formed by all angles measuring less than 90˚ is also known as an acute triangle. For example, in an equilateral triangle, all three angles measure 60˚, making it an acute triangle.

** Acute triangle**

### Fun Facts

1. At least two angles of any triangle are acute angles.

2. In a 180˚angle, if one angle is obtuse (more than 90˚), the other will always be an acute angle (less than 90˚).

## Solved Examples

**Question 1:** The measure of three angles is as follows:

- 75°
- 112°
- 17°

Mention the type of angle in each case.

**Answer:**

- Acute angle- since 75° is less than 90°
- Obtuse angle- since 112° is more than 90°
- Acute angle- since 17° is less than 90°

**Question 2:** Measure of some angles are given below:

∠A | ∠B | ∠C | ∠D | ∠E |

71° | 17° | 93° | 102° | 45° |

Find all the acute angles

**Answer: **The acute angles are: ∠A, ∠B, and ∠E as all these angles are less than 90°

**Question 3:**** **State *True *or *false*:

- An angle measuring 85° is an acute angle.
- An angle measuring 15° is an acute angle.

**Solution:**

- False
- True
- False
- True

## Practice Problems

## Acute Angle

### 1Determine the acute angles.

The first and second are acute angles because they are less than 90°.

### 2What would be formed when two rays share a common endpoint?

An angle is formed when two rays share a common endpoint.

### 3The angle with a measurement of 0° is called

There would be no angle formed with 0°. So, the answer would be option d.

## Conclusion

An acute angle is an angle that is less than 90°, and these angles can be measured using a protractor. In this lesson, we have learned about acute angles in a creative way. Discover and learn more interesting math topics at SplashLearn.

## Frequently Asked Questions

**How can we identify an acute angle?**

An angle with a measurement of less than 90° is called an acute angle. L shape forms 90° so if the arms of an angle open up less than an “L”, an acute angle is formed.

**What do you mean by acute triangle?**

An acute triangle is one in which each angle is less than 90°. Even if one angle of a triangle is 90° it is not an acute triangle. An equilateral triangle, for example, is always acute because all angles (60°) are less than 90°.

**What are the types of angles in geometry?**

The types of angles in geometry are as follows:

- The acute angle, which is greater than 0° but less than 90°
- The right angle, which forms a 90°

- The obtuse angle, which is greater than 90° but less than 180°
- The reflex angle, which is greater than 180° but less than 360°
- The complete angle, which forms a 360°