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Angles – Definition, Properties, Example,& Figures

Sep 20, 2022
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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: 

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°. 
Types of Angles:  

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. 
Unit Angle: 

Examples of angles with their measurements: 

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. 

parallel
Measure with Unit Angles 

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

Protractor 

parallel
  • 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. 

How to measure an angle with a protractor? 

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. 
How to measure an angle with a protractor? 2

Example: 

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

How to measure an angle with a protractor? 3
  • 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 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. 
60 degree

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? 

Add and Subtract Angle Measures 

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.
Find the following missing angles.
  1. Find the unknown angles from the figure below.
Find the unknown angles from the figure below.
  1. What is the value of x?
70 degree

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:  

Concept Map:  

Comments:

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