Geometry: Angles



In this lesson, 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:
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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 angle symbolABC. The vertex point is always given in the middle.

angle naming

 





How to name an angle



Have a look at the following video for another example on naming angles.:






Measuring Angles

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

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






The following video will show you 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

Solution:

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






The following video illustrates 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.






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