Acute Angle – Definition with Examples

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. 

Arms and Vertex 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°

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

Definition of An Acute Angle

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

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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.

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

  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.

Real-life Example of Acute Angle - slice of a pizza

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.

Real-life Example of Acute Angle - a wall clock at 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.

Real-life Example of Acute Angle - A pair of open scissors, alligator’s open mouth , and the beak of birds

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

                                               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:

  1. 75°    
  2. 112°    
  3. 17°

Mention the type of angle in each case.

Answer:

  1. Acute angle- since 75° is less than 90°
  2. Obtuse angle- since 112° is more than 90°
  3. 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:

  1.  An angle measuring 45° is a right angle.
  2.  An angle measuring 85° is an acute angle.
  3.  An angle measuring 90° is an obtuse angle.
  4.  An angle measuring 15° is an acute angle.

Solution:

  1. False
  2. True
  3. False
  4. True

Practice Problems

Acute Angle

Attend this Quiz & Test your knowledge.

1Determine the acute angles.

Acute Angle – Definition with Examples
I & III
I & II
II & IV
II & III
CorrectIncorrect
Correct answer is: I & II
The first and second are acute angles because they are less than 90°.

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

a ray
a line
a angle
a line segment
CorrectIncorrect
Correct answer is: a angle
An angle is formed when two rays share a common endpoint.

3The angle with a measurement of 0° is called

a complete angle
a right angle
a straight angle
None of these
CorrectIncorrect
Correct answer is: None of these
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

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.

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°.

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°