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Angle Measurement

Measurement of angles with protractors and addition of angles.

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Angle Measurement

Source: https://upload.wikimedia.org/wikipedia/commons/7/70/Protractor_Rapporteur_Degrees_V3.jpg
License: CC BY-NC 3.0

Harwin lives at the corner of a street. His street ends and another street begins at the corner. He sees the two streets on a map of the area and notices that his corner looks like the following figure. 

License: CC BY-NC 3.0

What is the measure (in degrees) of the angle formed by his street and the other street?

In this concept, you will learn about angle measurements.

Measuring Angles

Angles are measured in degrees. The larger the angle, the higher the number of degrees.

Angles are measured using a special tool called a protractor.

Here is a picture of a protractor.

License: CC BY-NC 3.0

Notice that you can see all of the degrees on the protractor.

Here are the steps for using a protractor.

  1. First, you line up the vertex with the little hole in the middle of the protractor, then carefully align the bottom ray with the bottom line of the protractor.
  2. Then, you follow the top ray to the number of degrees that the angle measures.

Let's look at an example.

License: CC BY-NC 3.0

Use a protractor to measure this angle.

First, line up your protractor to measure. Be sure that the vertex is at 0. Then write down each number of degrees.

120 degrees

Examples

Example 1

Earlier, you were given a problem about Harwin and his street corner.

His street corner looks like the following figure.

License: CC BY-NC 3.0

What is the measure (in degrees) of the angle formed by his street and the other street?

First, line up the hole in the middle of the protractor with the vertex.

Next, align the bottom ray with the bottom line of the protractor.

Then, follow the other ray and draw a line up to the angle measure.

90 degrees

The answer is 90 degrees.

Example 2

Is this angle larger than 90 degrees?

License: CC BY-NC 3.0

First, line up the hole in the middle of the protractor with the vertex and align the bottom ray with the bottom line of the protractor.

Next, look at the angle measure

120

Then, determine if that number is larger than 90 degrees.

Yes

The answer is that this angle is larger than 90 degrees.

Example 3

How many degrees are in a straight line?

License: CC BY-NC 3.0

First, line up the hole in the middle of the protractor with the vertex and align the bottom ray with the bottom line of the protractor.

Next, follow the other ray to the angle measure.

Then, write the angle measure.

180 degrees

The answer is 180 degrees.

Example 4

License: CC BY-NC 3.0

How would you use a protractor to determine the measure of this angle?

First, line up the hole in the middle of the protractor with the vertex.

Next, align the bottom ray with the bottom line of the protractor.

Then, follow the other ray and draw a line up to the angle measure.

The answer is to follow the other ray and draw a line up to the angle measure.

Example 5

License: CC BY-NC 3.0

What is the measure of this angle?

First, line up the hole in the middle of the protractor with the vertex.

Next, align the bottom ray with the bottom line of the protractor.

Then, follow the other ray and draw a line up to the angle measure.

35 degrees

The answer is 35 degrees.

Review

Draw the following angles. Be sure to use a protractor and check your work with a friend.

  1. 180 degrees
  2. 100 degrees
  3. 90 degrees
  4. 15 degrees
  5. 20 degrees
  6. 45 degrees
  7. 60 degrees
  8. 110 degrees
  9. 25 degrees
  10. 160 degrees
  11. 180 degrees
  12. 140 degrees
  13. 42 degrees
  14. 115 degrees
  15. 173 degrees

Review (Answers)

To see the Review answers, open this PDF file and look for section 9.4. 

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Image Attributions

  1. [1]^ Source: https://upload.wikimedia.org/wikipedia/commons/7/70/Protractor_Rapporteur_Degrees_V3.jpg; License: CC BY-NC 3.0
  2. [2]^ License: CC BY-NC 3.0
  3. [3]^ License: CC BY-NC 3.0
  4. [4]^ License: CC BY-NC 3.0
  5. [5]^ License: CC BY-NC 3.0
  6. [6]^ License: CC BY-NC 3.0
  7. [7]^ License: CC BY-NC 3.0
  8. [8]^ License: CC BY-NC 3.0
  9. [9]^ License: CC BY-NC 3.0

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