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. 

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. 

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∠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:

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

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