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 45° is a right angle.
- An angle measuring 85° is an acute angle.
- An angle measuring 90° is an obtuse 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°