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Acute Angles Explained with Examples

Acute Angles Explained with Examples

Q: 1. What is the exact definition of an acute angle in geometry?

An acute angle is an angle that measures more than 0° but less than 90°. It is visually recognised as being 'sharper' or 'narrower' than a right angle (which is exactly 90°). According to the CBSE/NCERT syllabus for the 2025-26 session, understanding this definition is a fundamental concept in geometry.

Q: 2. What are five common examples of acute angles?

Five common examples of acute angles based on their degree measurements are 30°, 45°, 60°, 75°, and 88°. Essentially, any angle that falls strictly between 0° and 90° is classified as an acute angle.

Q: 3. How can you easily identify an acute angle without a protractor?

You can easily identify an acute angle by its appearance. It looks smaller or 'sharper' than the corner of a square or a book. If an angle opens less than a perfect 'L' shape (which represents a 90° right angle), it is an acute angle. This visual check is a quick way to differentiate it from right and obtuse angles.

Q: 4. What are some examples of acute angles found in real life?

Acute angles are present in many everyday objects and structures. Common real-life examples include:The angle formed by the hands of a clock at 1 o'clock or 2 o'clock.The tip of a slice of pizza or a party hat.The 'V' shape made by a pair of open scissors.The pointed end of a pencil or a pen.The angles found at the vertex of a star.

Q: 5. What is the key difference between an acute angle, a right angle, and an obtuse angle?

The key difference between these three primary types of angles is their measurement:Acute Angle: Measures less than 90°.Right Angle: Measures exactly 90°.Obtuse Angle: Measures more than 90° but less than 180°.In simple terms, an acute angle is the sharpest, a right angle forms a perfect corner, and an obtuse angle is wider and more open than a right angle.

Q: 6. How do acute angles help in classifying different types of triangles?

Acute angles are fundamental to classifying triangles. A triangle where all three interior angles are acute (less than 90°) is called an acute-angled triangle or simply an acute triangle. For instance, an equilateral triangle, with all angles at 60°, is a perfect example of an acute triangle. This classification is a key topic in NCERT Maths.

Q: 7. Why is it impossible for a triangle to have only one acute angle?

A triangle must have at least two acute angles because of the Angle Sum Property, which states that the sum of a triangle's three interior angles is always 180°. If a triangle had only one acute angle (e.g., 40°), the other two angles would have to be right (90°) or obtuse (>90°). The sum of two such angles (e.g., 90° + 90° or 90° + 91°) would be 180° or more, leaving no degrees for the third angle, which violates the property.

Reviewed by:

Rama Sharma

What is an Acute Angle? Definition, Degrees & Key Examples

Angles are usually measured in degrees. An acute angle is a kind of an angle that measures between 0° and 90°, which means it is smaller than a right angle (L shape). An acute angle has a horizontal “V” shape. Acute angles are an elementary concept of geometry that have wide applications. There are three fundamental types of angles, and they are acute angle, right angle, and obtuse angle.

How to Remember Acute Angles?

Sometimes we get confused between the acute angles meaning and obtuse angles meaning. To remember the meaning of acute angle and identify it in an easy way, you can remember that the smallest angle in a triangle is an acute angle. We already know that the measure of an acute angle is less than 90°. Therefore, acute angle examples are 25°, 36°, 47°, 80°, and so on. Students can follow the formula of an acute angle to solve the sums of geometry.

Measurement of Acute Angles

An acute angle comprises two rays or line segments. The two-line segments meet at one endpoint of an acute angle. One line segment forms the base of the angle, while the line segment forms the arm of the angle. An acute angle can be measured by reading the angle measures on the protractor anti-clockwise. The acute angle can be constructed and measured with the help of a protractor. Acute angles are considered to be sharp angles. To have a precise idea about an acute angle degree diagrammatically, students can follow the image shown below.

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

The concept of acute angles plays a key role in mathematics and is widely applicable to both real-life situations and exam scenarios. Understanding acute angles helps students classify different types of angles, recognize shapes, solve geometry questions, and notice patterns in daily life.

What Is an Acute Angle?

An acute angle is defined as an angle that measures less than 90 degrees. You’ll find this concept applied in areas such as geometry, trigonometry, and even in real-world design patterns. Acute angles are often seen in triangles, polygons, and many everyday objects. They are the opposite of obtuse angles and smaller than a right angle.

Key Formula for Acute Angles

Here’s the standard rule: An angle is acute if 0° < angle < 90°

Angle Type	Measurement (Degrees)
Acute Angle	Less than 90°
Right Angle	Exactly 90°
Obtuse Angle	Greater than 90°, less than 180°

How to Identify Acute Angles Easily

Acute angles look "sharp" and "narrow" compared to right or obtuse angles. You can check any angle using a protractor—if it opens less than a perfect “L” shape (which is 90°), it’s acute. For example, angles of 30°, 45°, and 60° are all acute angles.

Acute Angles vs. Other Angles

Type	Symbol	Range (Degrees)	Example
Acute Angle	∠	0°–89°	30°, 45°, 60°
Right Angle	∟	90°	90°
Obtuse Angle	∠	91°–179°	110°, 135°
Straight Angle	—	180°	180°
Reflex Angle	∠	181°–359°	200°, 270°

Examples of Acute Angles with Diagrams

Here are some examples to help you recognize acute angles:

The angle formed at the tip of a “V” shape.
Slices of pizza make acute angles at the tip.
The hands of a clock at 2 o'clock.
Any triangle with all angles less than 90° (acute triangle).
A roof on a house makes two acute angles at the top.

Acute Angles in Triangles

If all three interior angles in a triangle are less than 90°, it is called an acute triangle. For instance, in an equilateral triangle, each angle is 60°—so it’s an acute-angled triangle. Some triangles can have a mix: one obtuse (greater than 90°) and two acute, but never only one acute angle in any triangle.

Frequent Errors and Misunderstandings

Thinking that all small-looking angles are acute without measuring.
Confusing acute and obtuse—remember: acute means less than 90°; obtuse means more than 90°.
Assuming a triangle can have only one acute angle (not possible).

Relation to Other Concepts

The idea of acute angles connects closely with topics such as types of angles and angle sum property. Mastering this helps with understanding polygons and more advanced triangle properties.

Try These Yourself

Write down three examples of acute angles found in your home.
Is the angle between the minute and hour hand at 1 o’clock acute or obtuse? Measure and check.
Draw a triangle with all angles less than 90°.
Spot an acute angle in your favorite English alphabet letter.

Classroom Tip

A quick way to remember acute angles: “Acute is a cute little angle”—it’s smaller and less than 90°. Vedantu’s teachers often use V-shaped fingers or clock examples to explain the concept in live classes.

We explored acute angles—from definition, formula, differences, shapes, examples, and quick memory tricks to help you get ready for tests. Keep practicing with Vedantu to become confident classifying and using all types of angles in maths!

Types and Properties of Acute Angle Triangle

A triangle in which all the three angles measure less than 90 ° is named an acute triangle. For example, in an equilateral triangle, all the three angles measure 60°, so it makes an acute angle. The properties of an acute angle triangle are listed below.

The interior angles of an acute angle triangle are always less than 90° with non-identical sides and measures.
In an acute triangle, the line constructed from the base of a triangle to the opposite vertex can be perpendicular to the base.
The perimeter of an acute triangle is the sum of the length of all three sides of a triangle.

Students can learn about different angles and triangles, acute angle triangles with solved examples and images on Vedantu. Below, a picture of an equilateral triangle is provided.

(image will be uploaded soon)

Acute Angle in Real Life

We can find acute angle examples in day-to-day life as well. Let us describe an elementary example. An example of an acute angle is there in a wall clock. The hands of a clock make acute angles at several hours a day. For example, if we consider 2 o'clock, the hour hand and minute hand form an acute angle at 2 o'clock. Similarly, if we slice a pizza into 5 or more slices, each slice of pizza makes an acute angle. The road signs, especially, “One way” and “No left turn” arrows also show an acute angle.

Acute and Obtuse Triangle

A triangle with all three angles less than 90° is named as an acute triangle. If you want to identify a triangle with obtuse angle, you must know about an obtuse angle. Obtuse triangles are described to have one obtuse angle, which is greater than 90°, and two acute angles. Refer to the below image to know about the structure of the obtuse angle triangle.

(image will be uploaded soon)

Acute Angles in a Right Triangle

A triangle that has a 90° angle is said to be a right triangle. The explanations of the acute angles of a right triangle are the angles that are opposite to the two shortest sides of the right triangle. If you want to learn how to find the acute angle between the lines, you can download the Vedantu app and refer to the study material and classes provided by our teachers. An acute angle has various applications in geometry. The acute angle notes on Vedantu will help you to understand and solve the sums of this topic.

FAQs on Acute Angles Explained with Examples

1. What is the exact definition of an acute angle in geometry?

An acute angle is an angle that measures more than 0° but less than 90°. It is visually recognised as being 'sharper' or 'narrower' than a right angle (which is exactly 90°). According to the CBSE/NCERT syllabus for the 2025-26 session, understanding this definition is a fundamental concept in geometry.

2. What are five common examples of acute angles?

Five common examples of acute angles based on their degree measurements are 30°, 45°, 60°, 75°, and 88°. Essentially, any angle that falls strictly between 0° and 90° is classified as an acute angle.

3. How can you easily identify an acute angle without a protractor?

You can easily identify an acute angle by its appearance. It looks smaller or 'sharper' than the corner of a square or a book. If an angle opens less than a perfect 'L' shape (which represents a 90° right angle), it is an acute angle. This visual check is a quick way to differentiate it from right and obtuse angles.

4. What are some examples of acute angles found in real life?

Acute angles are present in many everyday objects and structures. Common real-life examples include:

The angle formed by the hands of a clock at 1 o'clock or 2 o'clock.
The tip of a slice of pizza or a party hat.
The 'V' shape made by a pair of open scissors.
The pointed end of a pencil or a pen.
The angles found at the vertex of a star.

5. What is the key difference between an acute angle, a right angle, and an obtuse angle?

The key difference between these three primary types of angles is their measurement:

Acute Angle: Measures less than 90°.
Right Angle: Measures exactly 90°.
Obtuse Angle: Measures more than 90° but less than 180°.

In simple terms, an acute angle is the sharpest, a right angle forms a perfect corner, and an obtuse angle is wider and more open than a right angle.

6. How do acute angles help in classifying different types of triangles?

Acute angles are fundamental to classifying triangles. A triangle where all three interior angles are acute (less than 90°) is called an acute-angled triangle or simply an acute triangle. For instance, an equilateral triangle, with all angles at 60°, is a perfect example of an acute triangle. This classification is a key topic in NCERT Maths.

7. Why is it impossible for a triangle to have only one acute angle?

A triangle must have at least two acute angles because of the Angle Sum Property, which states that the sum of a triangle's three interior angles is always 180°. If a triangle had only one acute angle (e.g., 40°), the other two angles would have to be right (90°) or obtuse (>90°). The sum of two such angles (e.g., 90° + 90° or 90° + 91°) would be 180° or more, leaving no degrees for the third angle, which violates the property.

8. What are the main properties of an acute angle?

The main properties that define an acute angle in geometry are:

Its measure is always greater than 0 degrees and less than 90 degrees (0° < θ < 90°).
It is always smaller than both a right angle (90°) and an obtuse angle (>90°).
The complement of an acute angle is always another acute angle (since their sum must be 90°).
In any triangle, there are always at least two acute angles.

9. Can an angle be both acute and a right angle at the same time?

No, an angle cannot be both acute and right. These categories are mutually exclusive by definition. An angle is classified as acute only if it is strictly less than 90°. In contrast, a right angle must be exactly 90°. There is no value that satisfies both conditions simultaneously.