Geometry: Angles

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.

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.

Have a look at the following video for another example:

Measuring Angles

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

A straight line has an angle of 180°

Angles Around A Point

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

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.

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°

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