Acute Angles

Dhristi JEE 2022-24

Acute Angles in Detail

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.


Acute Angle

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

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.


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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.


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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

1. What are the Five Types of Angles?

Ans. The five types of angles are acute angle (< 90°), obtuse angle (> 90°), right angle (= 90°), straight angle (= 180°), reflex angle (> 180°). There is another angle which measures 360° and is called full rotation of the axis.

2. Can a Triangle Have Only One Acute Angle?

Ans: No, a triangle cannot have only one acute angle. If a triangle has 1 obtuse angle, the other two angles will have to be either right angles or obtuse angles. It is not possible as the summations of interior angles of a triangle are always 180°. So, every triangle requires at least 2 acute angles.

3. How Can You Measure Angles?

Ans: Angles can be measured by using a protractor. First, we need to place the center of the protractor at a fixed point. We can consider one arm of an angle as the base. When we measure from the base of the angle in an anti-clockwise manner till the other arm, we will get the degree of the angle.