# Acute Angle – Definition, Types, Examples, FAQs

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## 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.

## 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.

## 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°

## 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

## 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 On Acute Angle

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

1. 75°
2. 112°
3. 17°

Mention the type of angle in each case.

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:

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 On Acute Angle

1

### Determine the acute angles.

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°.
2

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

a ray
a line
a angle
a line segment
CorrectIncorrect
An angle is formed when two rays share a common endpoint.
3

### The 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 On 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.

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°