Angles – Definition, Properties, Example,& Figures

Key Concepts

• To understand angles and unit angles
• To measure with unit angles
• To measure and draw angles
• To add and subtract angle measures

Understand Angles and Unit Angles 

Angle: 

An angle is the rotation of a ray from an initial point to a terminal point. 

Types of Angles:  

There are majorly six types of angles in geometry: 

• Acute angle: It lies between 0° to 90°. 
• Obtuse angle: It lies between 90° to 180°. 
• Right angle: The angle which is exactly equal to 90°. 
• Straight angle: The angle which is exactly equal to 180°. 
• Reflex angle: The angle which is greater than 180° and less than 360°. 
• Full rotation: The complete rotation of an angle equal to 360°. 

Unit Angle: 

• An angle is measured with units called degrees (ᵒ). 
• An angle that turns through 1 / 360 of a circle is called a unit angle. 

Examples of angles with their measurements: 

Measure with Unit Angles 

Unit angles are measured using a smaller angle to measure a larger angle by repeating the unit. 

Unit angle 

Example: 

What is the measurement of the smaller angle formed by the clock hands when it is 5 o’clock? 

Measure and Draw Angles 

Measuring angles with a protractor 

Angles are measured in degrees. The symbol for degrees is a small circle °. 

Protractor 

• The full circle is 360° (360 degrees). 
• A half-circle or a straight angle is 180°. 
• A quarter-circle or a right angle is 90°. 

How to measure an angle with a protractor? 

A protractor is a tool that is used to measure and draw angles. 

Protractor 

• Place the midpoint of the protractor on the vertex of the angle.  
• Line up one side of the angle with the line zero of the protractor 
  (Where you see the number 0). 
• Read the degrees where the other side crosses the number scale. 

Example: 

Draw ∠ABC=60° with a ruler and a protractor. 

• Draw a straight-line AB. 
• Place a dot at B.  This dot represents the vertex of the angle. 
• Place the center of the protractor at B and the baseline of the protractor along with the arm BA. 
• Find 60° on the scale and mark a small dot at the edge of the protractor. 
• Join the vertex B  to the small dot with a ruler to form the second arm, BC, of the angle. 
• Mark the angle with a small arc as shown. 

Add and Subtract Angle Measures 

Finding the measure of an unknown angle by using the known measures. 

If ∠ABD = 107°, what is the measure of ∠ABC? 

We know that: 

∠ABC + ∠CBD = ∠ABD 

Plug in the known: n + 37° = 107° 

Use the inverse operation to isolate the variable n = 107° – 37° = 70° 

So, ∠ABC = 70°. 

Exercise:

1. Use a protractor to draw an angle measure for 65⁰.
2. How many 60⁰ angles does it take to make a full turn?
3. How many degrees are in a twelfth of a full turn?
4. What fraction of the circle does a 120⁰ angle turn through?
5. What are the measures of an angle?
6. What are the 5 types of angles?
7. What is a zero angle?
8. Find the following missing angles.

9. Find the unknown angles from the figure below.

10. What is the value of x?

What have we learnt:

• To use and apply vocabulary associated with angles.
• To identify examples of different types of angles.
• To measure and draw angles with a protractor.
• To understand angles and unit angles.
• To add and subtract angle measures.

Concept Map: