Acute Angle - Definition with Examples

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What is Acute Angle?

In geometry, two rays sharing a common endpoint form an angle. The common endpoint is called the vertex, and the two rays are called the arms of the angle. 

acute angle


Types of Angles

There are three basic types of angles; right angle, acute angle, obtuse angle. 



Definition of an acute angle:  

An acute angle is an angle that measures less than 90 degrees. 

define acute angle

∠ABC measures 30 ̊and hence it is an acute angle


A triangle formed by all angles measuring less than 90˚ is also known as an acute triangle. For example, in an equilateral triangle, all three angles measure 60˚, making it an acute triangle.

acute triangle
                                                         Acute triangle 


Dividing the right angle will give us two or more acute angles since each newly formed angle will be less than 90˚.

  • Right Angle

  • Two acute angles formed by dividing the right angle

divide right angle


Some real-life examples of acute angles are:

If we slice a pizza into 5 or more slices, each slice of pizza will make an acute angle.

real life example of acute angle 

Each slice of the pizza makes an acute angle.


Another example is the wall clock. The arms of a wall clock make acute angles at several hours of a day.  For example, 2 o’ Clock.

real life example of acute angle 1

The hour hand and the minute hand forming an acute angle at 2 o’ Clock.

  Fun Facts

  • At least two angles of any triangle are acute angles.
  • In a 180˚angle, if one angle is obtuse (more than 90˚), the other will always be an acute angle (less than 90˚).

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