Acute Angle – Definition, Diagrams, Examples, Properties, and Formula

acute angle

Whenever you see an angle and it measures less than 90 degrees then affirm it as the acute angle. An acute angle is formed by the two arms of the clock when the time is 11 o’clock. Thus, this simply means that all other angles (30, 40, 60 degrees) which are less than 90 degrees.

How Would You Define an Acute Angle?

Do you know how an angle is formed? An angle is formed when two rays meet at a point which is known as the vertex point. When this angle is measured and the result comes as less than 90 degrees, then this is known as the acute angle.

Drawing Two Acute Angle in a Diagram of Two Rays

Follow these steps which will help us to identify acute angles in a two-ray diagram. The steps are as follows:

  • Suppose, there are two rays – Ray 1 and Ray 2.
  • When these two rays meet at a vertex, an angle is formed.
  • This angle is measured and the result comes as 90 degrees.
  • Now the 90-degree angle is cut at the vertex.
  • After this division, two angles are formed which measures less than 90 degrees.
  • Here you have two acute angles measuring less than 90 degrees.

What are the Different Measurement of an Acute Angle?

As studied, we know what is an acute angle. As explained, angles measure less than 90 degrees. Therefore, the angles which are less than 90 degrees will be – 63°, 31°, 44°, 68°, 83°, 85°.

We see that the acute angle degrees will range from 0 to 90 degrees. Thus, this can be more than 0 degrees but less than 90 degrees.

Examples of Acute Angles

A few examples of acute angles from real life are as follows:

  • Slice of melon when cut into small divisions.
  • At times angles are formed by the clock also take the measurement of 90 degrees.
  • The curved beak of the crow or any other bird.
  • The angle is formed when the alligator opens its mouth to catch its prey.

What are the Properties of an Acute Angle?

The properties of the acute angle are:

  1. The acute angle has angles that measure less than 90 degrees.
  2. Acute angles can form Triangles, which will measure less than 90 degrees.
  3. This will also form acute scalene triangles, acute isosceles triangles, and equilateral triangles.

How Would you Derive the Acute Angle Formula?

We know the Pythagoras Theorem formula which is curated for the right-angled triangles, now for the acute angle triangle, we have the formula which is popularly known as the triangle of inequality formula which is for acute angle triangles.

The formula states that the sum of the squares of any two sides of a triangle being greater than the square of the largest side, then it shall be proved that it is an acute-angled triangle.

Study From Cuemath

Cuemath will help your kids to logically understand maths. Cuemath is known as the leading live online class for maths, thus it is ensured that the students will be guided in the field of Mathematics, like nowhere else.

This is a common tendency of students lacking excellence in Maths, or fear in the subject Maths. The prime reason for this is less conceptual understanding. In Cuemath, it is assured that the students know the topic conceptually and logically. Sums are also practiced based on each of the topics. Like in the studied topic – Acute Angle, we studied clearly and conceptually the definition, properties, and examples of Acute Angle.

Students are further suggested to practice the sums which they have learned previously and do exercises which will help them to understand the chapter better.

You can visit Cuemath for more detailed experience in Maths.

Also Read: How many sides does a Pentagon have ?


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