Session 2: Angles – Definition, Types, Interactives and Examples

What is an Angle?

• When two rays meet at their endpoints, they form an angle.
• Depending on the situation, an angle can be named with an angle symbol ∠ and its vertex, or by three letters.

If three letters are used, the middle letter should be the vertex. The angle below could be called ∠B or ∠ABC, or ∠CBA. Use three letters to name an angle if using one letter does not clarify what angle you are talking about.

Explain why you must use three letters to identify any of the angles in the diagram below.

All angles in this diagram have a vertex of E. Therefore ∠E is ambiguous because it could refer to many different angles. Use three letters with E as the middle letter to clarify which angle you are referring to ∠AEC, ∠AED, ∠DEB, ∠BEC.  

Interior and Exterior of an Angle

All the points on the plane of ∠CBD can be divided into three groups:

1. Points that lie within the arms of the angle produced indefinitely. 
2. Points that lie on the arms of the angle produced indefinitely. 
3. Points that lie outside the arms of the angle produced indefinitely.  

Part of the plane which lies between ray BC and ray BD. This part is known as the interior of ∠CBD. 

Part of the plane which does not lie between ray BC and ray BD. This part is known as the exterior of ∠CBD.   

The Measure of an Angle

The size of an angle depends on how far apart the rays are from each other. There are several different units for measuring the space between the arms. One unit of angle measurement is degrees, which can be measured with the protractor or geometry software. Remember that a full circle includes 360 degrees . 360 degrees can also be written as 360∘.

Types of Angles

• An angle that is exactly 0∘is called a zero angle.
• An angle that is less than 90∘is called an acute angle.
• An angle that is exactly 90∘(one-quarter of a circle) is called a right angle. A right angle is noted with a little square at its vertex.
• An angle that is more than 90∘ but less than 180∘ is called an obtuse angle. An angle that is exactly 180∘(one half of a circle) is called a straight angle.

• An angle that is more than 180∘ and less than 360∘ is called a reflex angle.

Angles – Examples

Example 1

Name all angles formed in the adjoining figure. 

There are six angles found in the figure. The angles are .

Example 2

Name each angle in three ways. 

 Remember this!

• The inclination between two rays having a common endpoint is called an angle. 
• An angle that is exactly 0∘ is called a zero angle. 
• An angle whose measure is more than 0∘ but less than 90∘ is called an acute angle. 
• An angle that is exactly 90∘ (one-quarter of a circle) is called a right angle. 
• An angle that is more than 90∘ but less than 180∘ is called an obtuse angle. 
• An angle that is more than 180∘ and less than 360∘ is called a reflex angle.