An angle smaller than the right angle is called an acute angle. In other words, the angle which is less than 90 degrees forms an acute angle. The polygons such as triangles, parallelograms, trapezoids, etc. consist of at least one acute angle. Let us learn here some basics of angles.
The two lines or line segments or rays with a common point lead to the formation of an angle. An angle is denoted through a symbol ‘∠’. An angle is measured with the help of a protractor in degrees (o).
- Vertex: A corner or a point where lines meet is called the vertex of an angle.
- Arms: The two lines that meet to make an angle are called arms of an angle.
- Measuring Angle: Angles can be measured using a protractor.
- Place the center of the protractor at a fixed point, say O of the angle at one of the arms.
- Another arm indicates the degree of the angle while measured from the initial hand in an anti-clockwise manner.
Acute Angle Definition
An angle which is measuring less than 90 degrees is called an acute angle. This angle is smaller than the right angle (which is equal to 90 degrees). For example, ∠30o, ∠45o, ∠60o, ∠75o, ∠33o, ∠55o, ∠85o, etc. are all acute angles. Let us see some examples here to understand.
∠ABC measures 30 degrees, which is less than 90 degrees and hence it is an acute angle.
The basic types of angles are right angle, obtuse angle, and acute angle. we can differentiate between the three angles. The first figure shows an acute angle measuring 62 degrees (less than 90 degrees), the second figure shows a right angle measuring 90 degrees and the third figure shows an obtuse angle measuring 135 degrees (more than 90 degrees).
Note: Dividing the right angle gives us two or more acute angles since each angle formed, there will be much less than 90˚.
Acute Angle Degree
The degree of an acute angle measures less than 90 degrees, i.e. less than a right angle. The examples of acute angle degrees are 12°, 35°, 48°, 65°, 80°, 89°. Hence, the acute angle degree ranges from 0 degrees and less than 90 degrees.
Acute angle Images
The below figure shows the images of acute angles measuring 40 and 60 degrees
Can two acute angles form a linear pair?
No, since the measure of a linear pair of angles should be 180 degrees and the measure of an acute angle is less than 90 degrees. Therefore, two acute angles will not form a linear pair. For example, 85° and 75° are two angles such that 85° + 75° = 160° < 180°. Thus, 85° and 75° do not form a linear pair.
Acute Angle Formula
In an acute triangle, the following statement holds good for the length of the sides:
a2 + b2 > c2
b2 + c2 > a2
c2 + a2 > b2
Where a, b, and c are the sides of a triangle.
