How to Measure Angles

To help learn how to measure angles take a look at the two clocks that are shown here. The red line segments that are drawn over the hands of the clocks are the sides of the angles.

The measure of the angles deals with the distance between the two hands of the clock. In this example, the clock on the right has a great distance between the two hands. This translates to a larger angle measurement.

The most common way to measure an angle is by degrees. In a full circle, there are 360° - which means that a half circle is 180°. In geometry, we deal with angles between 0° and 180°. Take a look at the examples below.

The Largest and Smallest Angles

Use the following colors to understand the examples below:

  • First side of the angle

  • Second side of the angle

  • Vertex of the angle



When both sides of the angle are on top of each other, the angle is 0°. In this particular case, there is no space between the two sides.

When both sides of the angle are completely opposite each other, the angle is 180°. In this case, the angle forms a straight line and is known as a straight angle.

We are interested in determining how far apart the two sides of the angle are when they are in between 0° and 180°.

How to Measure Angles-The Protractor

A protractor is the most common tool used to measure angles and looks like the picture shown below.

To use a protractor, locate the hole in the center of the ruler at the bottom.

You want to place the hole of the protractor right on top of the vertex of the angle. Once you've done, line up one side of the angle with the line drawn on the protractor.


Take a look at the first example. Notice how the red side of the angle is straight
along the line on the protractor.

Now, take a look at the blue side of the angle. What numbers on the protractor does the blue line touch?

The blue line goes across the numbers 40° and 140°. To choose between the two angles, you must know the difference between acute and obtuse angles - take a look now if you need to. Because this is an acute angle, its measurement is 40°.

Another Example

Again, we lined up the red side of the angle along the line on the bottom of the protractor. We put the hole in the protractor above the vertex. What numbers does the blue side cross?

Answer: 80°

Hopefully you now know how to measure angles. For other great geometry lessons, return to the geometry free help page.

You may also return from "How to measure angles" to the Grade A homepage for other great mathematics resources.



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