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Acute Angle|Definition & Meaning

Definition

An acute angle is one that is smaller than 90 degrees and greater than 0 degrees.

If the measured angle between two arrays is less than 90 and greater than 0, the angle will be named an Acute angle. The term acute indicates that this angle is small. So, here it shows that the measured angle is smaller than 90.

For example, you measure the angle between two joined arrays drawn on paper using a protractor. You find that the angle between these two arrays is 50 degrees. As this value is less than 90 degrees and more than 0 degrees, so you can say that it is an acute angle.

 

 

The angle in figure one is an acute angle as it is less than 90 degrees.

Let us try to understand acute angles from scratch. For that, we first understand what an angle is.

Angle

An angle is formed by the joining of two line segments or rays. They can join in any direction with a single common end. The measure of an angle is defined by the difference in direction of these two line segments. 

The Symbol used to represent an angle is ‘∠’ and the tool that is used to measure the angle is called a protector. The standard unit of angle is degrees. It can also be measured in radians.

The common point of two line segments or rays where these lines join each other is known as the Vertex. And these two lines which join to form an angel are known as Arms on an angle.

Angles have many different types, but the basic three types are Acute angle, Obtuse angle, and right angle. In this article, we will discuss the acute angle.

Acute Angle

If the measure of degrees in angle is less than 90 degrees, the angle will be acute. We can also say that if an angle is smaller than a right angle, it is an acute angle.

Acute angles can not form a linear line or pair because a linear pair is formed when the angle is 180 degrees. As the acute angle cannot be equal to or more than 90 so, even if two acute angles are added, they can not form a linear pair.

Acute Angle Triangle, Parallelogram and Trapezoid

An acute angle triangle is a triangle whose all internal angles are acute angles. If a triangle has all the sides of equal length i.e equilateral triangle then all the internal angles will be less than 90 degrees so it will be an acute triangle.

An Acute angle parallelogram is a parallelogram in which the two internal angles are acute and two are obtuse. A parallelogram has two opposites in equal length.

The trapezoid also has two acute angles and two obtuse angles in which there is one parallel pair.

Real-Life Applications of Acute Angles

If we ponder the things around us, we can find a variety of things in which there is an acute angle. The wall clock hanging on the wall of our house at times like  2 o clocks shows an acute angle.

Alphabet ‘V’ in English makes an acute angle at the junction point. Similarly, if we divide a cake into four or more parts, each part of the cake will form an angle less than 90 degrees i.e. acute angle.

Many traffic signs like link road joining the main road, one way, etc form acute angles. The speedometer of our vehicles at low speed forms an acute angle with the left indicator and at high speed, it forms an acute angle with the right indicator.

Further Illustrations

 
An angle of five degrees is an acute angle

Figure 2 – Angle between two rays showing an Acute angle of 5 degrees

The angle shown in figure two is less than 90 degrees which tells that it is an acute angle.

A barely acute angle at eighty-nine degrees

Figure 3 – Angle between two rays showing an Acute angle of 89 degrees

The angle shown in Figure 3 is not exactly 90 degrees rather it is 1 degree less than 90 degrees. So, it is also an acute angle.

An acute angle in a triangle

Figure 4 – Angle between two sides of triangle  showing an Acute angle of 38 degrees

In figure 4 the angle formed at point B of the triangle is 38 degrees which are less than 90 degrees. So is the case with the other two angles, they are also less than 90 degrees. Such a triangle is an acute angle triangle.

Real-life Example

Students of grade I are assigned a task. They are provided with a protector to measure angles of different shapes. The following values were noted by the students. Indicate whether these are acute angles or not.

Values are 18 degrees, 29 degrees, 91 degrees, 101 degrees, 83 degrees, 89 degrees, and 99 degrees.

Solution

18 Degrees: As 18 degrees is smaller than 90 degrees, it is an acute angle.

29 Degrees: As 29 degrees is smaller than 90 degrees, it is an acute angle.

91 Degrees: As 91 degrees is not less than 90 degrees, it is not an acute angle.

101 Degrees: As 101 degrees is not less than 90 degrees, it is not an acute angle.

83 Degrees: As 83 degrees is smaller than 90 degrees, it is an acute angle.

89 Degrees: As 89 degrees is smaller than 90 degrees, it is an acute angle.

99 Degrees: As 99 degrees is not less than 90 degrees, it is not an acute angle.

105 Degrees: As 105 degrees is not less than 90 degrees, it is not an acute angle.

360 Degrees: As 360 degrees is smaller than 90 degrees, it is not an acute angle.

1 Degree: As 1 degree is smaller than 90 degrees, it is an acute angle.

33 Degrees: As 33 degrees is not less than 90 degrees, it is not an acute angle.

All mathematical images are created using GeoGebra.

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