Exams Academic Acute Angle: Definition, Degree, Formula, Types, and Examples

Written By Varsha
Last Modified 30-01-2023

Acute Angle: Definition, Degree, Formula, Types, and Examples

Acute Angle: In Mathematics, two lines intersect at a point to form an angle. There many types of angles in Geometry such as Acute, Obtuse, Right, etc. The acute angle is the angle that is less than 90°. Polygons such as Triangle, Parallelogram, Trapezoid, etc. will have at least one acute angle.

On this page, we have provided all the necessary information on what is an acute angle along with definitions, formulas, and examples. Read on to find out more.

What Is Acute Angle?

Acute Angle Definition: An angle that is less than 90° is known as an acute angle. The acute angle is otherwise called the angle which is less than the right angle. The acute angle is denoted by the symbol ‘∠’ and measured with the help of a protractor in terms of degree.

Acute Angle Examples: Few examples of acute angles in degrees are ∠80^o, ∠55^o, ∠70^o, ∠25^o, ∠83^o, ∠89^o, ∠15^o, ∠12^o, ∠28^o.

A ∠45^o acute angle can be sketched as follows:

Acute Angle Representation

Every angle has two components: Sides and Vertex. Similarly, the acute angle also has two components sides and vertex. The representation of the acute angle.

Vertex: A point where two lines intersect is known as Vertex.
Arms: Arms are the segmentation or the two lines which originate from a vertex to create an angle.

Acute Angle Triangle

If the internal angles of a triangle are less than 90 degrees then it is known as an acute angle triangle. Equilateral triangles have acute angles.

Acute Angle Parallelogram

A Parallelogram is nothing but a quadrilateral whose opposite sides are parallel and equal. Each and every parallelogram has two acute angles whose angle is less than 90 degrees.

Here ∠SPQ and ∠QRS are acute angles.

Acute Angle Trapezoid

A Trapezoid is a parallelogram with a pair of opposite sides parallel to each other. Each trapezoid has 2 acute angles.

Here ∠DCB & ∠ADC are acute angles.

Acute Angle Formula

For an acute-angled triangle, the following holds good for the lengths of the sides:

q² + p² > r²
p² + r² > q²
r² + q² > p²

Where p, q, and r are the lengths of the sides.

Properties Of An Acute Angle

The properties of acute angles are given below:

Dividing one right angle gives us two or more acute angles.
All equilateral triangles are acute angle triangles.
Any angle which is more than 90 degrees doesn’t fall under the acute angle category.
Two angles of any triangle will be acute angles.

Acute Angle Examples In Real Life

Few real-life examples of acute angles are given below:

Letter V makes an acute angle
When the clock strikes at 1 or 2 o’clock, it forms an acute angle
The pizza slice forms an acute angle
Few roads signs which show directions form acute angles
Few exercise postures form acute angles

Acute Angle Questions

Few solved questions on acute angles are given below:

Q.Which of the following is a possible acute angle measurement?
Options:
90 degrees
45 degrees
180 degrees
360 degrees
Answer: 45 degrees is an acute angle.

Q. Which of the following letters contains an acute angle?
Options:
E
F
H
V
A. Letter “V” contains an acute angle.

Q. Is 1 O’Clock an acute angle?
A. Yes, 1 O’Clock is an acute angle.

Q. What is an acute angle?
A. An angle between 0 and 90 degrees is known as acute angles.

Q. Is 0 degrees acute angle?
A. Yes, 0 degree is acute angles.

Q. Write 5 examples of acute angle degrees?
A. The 5 examples of acute angles in degrees are ∠70^o, ∠25^o, ∠83^o, ∠89^o, ∠15.

You can also make use of Class 6 Maths Practical Geometry NCERT Solutions which will be helpful in your exam preparation.

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