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Geometry: Angles

In these lessons, we will learn the following:
  • How to form an Angle
  • Naming an Angle
  • Measuring Angles with a protractor
  • Angles around a point (with worksheets)
Related Topics: More Geometry Lessons
Geometry Worksheets
Geometry Games

How to form an Angle

In geometry, an angle consists of two rays that share the same endpoint. The point where the rays intersect is called the vertex of the angle. The two rays are called the sides of the angle.

angle definition

Naming An Angle

You can name an angle by specifying three points: two on the rays and one at the vertex.

The angle below may be specified as angle ABC or ∠ABC. The vertex point is always given in the middle.

angle naming

How to name an angle?
The vertex is the point where the two rays meet to form an angle.
Angles can be named in three ways:
1. By three capital letters, with the vertex letter in the middle. ∠ABC or ∠CBA
2. By one capital letter ∠B. This can only be used if ∠B is the only angle it could be.
3. By one lower case letter or number written in the middle of the angle.
Have a look at the following video for another example on naming angles
Name the vertex and and sides of ∠4, and give all possible names for ∠4.

Measuring Angles

The size of an angle is measured in degrees with the use of a protractor.


right angle   acute angle 40 deg   obtuse angle

A straight line has an angle of 180°

straight line

Worksheets for Angles in a straight line

How to use a protractor to measure an angle? How to Measure a Reflex Angle Using a Protractor?


Angles Around A Point

The sum of angles around a point will always be 360 degrees.

angles around  point

In the diagram above, the sum of the angles is 70° + 55° + 50° + 65° + 120° = 360°

Example 1: Given the diagram below, determine the value of the angle a.

angles around point


Step 1: Get the sum of the known angles.

30° + 65° + 150° + 73° = 318°

Step 2: Subtract sum of known angles from 360°

360° – 318° = 42°

Answer: Angle a is 42°

Worksheets for Angles Around a Point

What are angles around a point?
It will also give some examples of finding angles around a point. Problem Solving: Angles Around a Point
This video discusses relationships among angles around a point.

Rotate to landscape screen format on a mobile phone or small tablet to use the Mathway widget, a free math problem solver that answers your questions with step-by-step explanations.

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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