How To Make Angles In Math Using A Protractor: 13 Steps - WikiHow

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Terms of Use wikiHow is where trusted research and expert knowledge come together. Learn why people trust wikiHow How to Make Angles in Math Using a Protractor PDF download Download Article Explore this Article parts 1 Understanding the Features of a Protractor 2 Classifying Angles 3 Drawing an Angle Other Sections Questions & Answers Video Tips and Warnings Related Articles Expert Interview References Reviewed by Taylor Klein

Last Updated: July 13, 2025 Fact Checked

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This article was reviewed by Taylor Klein. Taylor Klein is an Advanced Math Teacher based in Philadelphia, Pennsylvania. She has worked in the education field for over 10 years, including eight years as a middle school Advanced Math Teacher. She has a master’s degree in Instructional Technology and Design and a master’s degree in Educational Leadership and Administration. There are 10 references cited in this article, which can be found at the bottom of the page. This article has been fact-checked, ensuring the accuracy of any cited facts and confirming the authority of its sources. This article has been viewed 78,225 times.

Using a protractor can be tricky, especially if you are using one with two sets of numbers. If you understand the concept of acute and obtuse angles, however, learning how to use a protractor is easy. It is first necessary to understand the features on a protractor, so that you understand how to use it. Once you have this understanding, you can quickly use a protractor to make any size angle between 0 and 180 degrees.

Steps

Part 1 Part 1 of 3:

Understanding the Features of a Protractor

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  1. Step 1 Locate the base line. 1 Locate the base line. This horizontal line is at the bottom of the protractor. One vector of your angle should always line up with the base line.[1]
    • Since a straight line is 180 degrees, the base line marks a 180-degree angle.
  2. Step 2 Locate the origin hole. 2 Locate the origin hole. This is a small hole at the midpoint of the base line. You use this hole to create the vertex of the angle. The vertex is the point at which the two vectors meet, creating an angle.[2] Advertisement
  3. Step 3 Locate the degree measurements. 3 Locate the degree measurements. Most protractors have two sets of numbers, an outer set and an inner set. Which set of numbers you use will depend on whether your angle opens to the right, or opens to the left. The sets of numbers can be set up differently on each protractor, so you need to figure out for yourself which set of numbers to use. To determine which set of numbers to use, you need to understand right, acute, and obtuse angles.[3]
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Part 2 Part 2 of 3:

Classifying Angles

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  1. Step 1 Identify a right angle. 1 Identify a right angle. A right angle has a measurement of 90 degrees.[4] A 90-degree angle will look like the corner of a square.[5] The two vectors of the angle are perpendicular, and open exactly halfway towards a straight line (which is 180 degrees).
    • When you line up the base line of the protractor with one vector of a right angle, the other vector will line up with the 90-degree mark of the protractor. This is halfway between either side of the protractor. Both the inner and outer sets of numbers on the protractor will show 90 degrees at this point.
  2. Step 2 Identify an acute angle. 2 Identify an acute angle. An acute angle has a measurement of less than 90 degrees.[6] This means that the two vectors will be closer together than they are in a 90-degree angle. They will open less than halfway towards a straight line. If the angle you are drawing is less than 90 degrees, make sure you use the set of numbers that gives you the smaller angle.[7]
    • For example, a 45-degree angle is acute, because 45 is less than 90. If you line up the base line of the protractor with one vector of a 45-degree angle, the other vector will line up with the 45-degree mark and the 135-degree mark of the protractor. You will know which line to look at because you know it is an acute angle, and an acute angle should be less open than a 90-degree angle.
  3. Step 3 Identify an obtuse angle. 3 Identify an obtuse angle. An obtuse angle has a measurement of more than 90 degrees.[8] The two vectors of an obtuse angle are farther apart than they are in a 90-degree angle. They will open more than halfway to a straight line. If the angle you are drawing is more than 90 degrees, make sure you use the set of numbers that gives you the larger angle.[9]
    • For example, a 120-degree angle is obtuse, because 120 is greater than 90. If you line up the base line of the protractor with one vector of a 120-degree angle, the other vector will line up with the 120-degree mark and the 60-degree mark. If you know you are looking for an obtuse angle, you know to use the 120-degree mark, because an obtuse angle should be more open than a 90-degree angle.
  4. Step 4 Ignore the orientation of the angle. 4 Ignore the orientation of the angle. Whether an angle opens to the left or to the right does not affect whether it is right, acute, or obtuse. All that matters is the measurement of the angle in degrees. The way the angle opens only changes the set of numbers you will look at on your protractor.[10]
    • For example, if a 45-degree angle opens to the right, you might have to look at the inner set of numbers. But if you were to turn that angle around so that it opens to the left, it would still measure 45 degrees, but this time when you measure it, you would have to look at the outer set of numbers.
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Part 3 Part 3 of 3:

Drawing an Angle

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  1. Step 1 Determine the measurement of the angle you are drawing. 1 Determine the measurement of the angle you are drawing. Note whether the angle is acute or obtuse.
    • For example, you might need to draw a 45 degree angle. Since 45 is less than 90, this is an acute angle. That means you will use the set of numbers that gives you the smaller angle, since the angle will open less than halfway towards a straight line.
  2. Step 2 Draw a straight line. 2 Draw a straight line. You can do this using a ruler or the straightedge of your protractor. This line will form the first vector of your angle.[11]
    • The length of the line does not necessarily matter, but the longer it is, the easier it will be to line it up to the base line. The best method is to draw a line running the length of the protractor’s edge.
  3. Step 3 Align the origin hole at about the midpoint of the line. 3 Align the origin hole at about the midpoint of the line. Make sure that the base line of the protractor lines up with the line you drew.[12] Draw a midpoint for your reference.
  4. Step 4 Mark the angle measurement. 4 Mark the angle measurement. Make this mark along the outside of the protractor by the appropriate degree mark. To make sure you are making the mark at the correct place, ask yourself the following questions:
    • Will my angle open to the right, or to the left?
    • Is my angle less (acute) or greater (obtuse) than 90 degrees?
  5. Step 5 Draw the second vector of the angle. 5 Draw the second vector of the angle. Use a ruler or straightedge to join the origin point on the base line to the degree mark.[13]
  6. Step 6 Erase any unnecessary lines. 6 Erase any unnecessary lines. You will likely need to erase part of the base line you drew. Otherwise, you may have two angles drawn, and it may be unclear to another person which is your intended angle.
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Community Q&A

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  • Question What are angles opening to the left called? Community Answer Community Answer The type of angle is not determined by which way it opens. An angle is either acute, right, or obtuse, no matter which way it opens. All that matters is the size of the angle. For example, you can draw a 45 degree angle opening to the left, or opening to the right. Either way, it is an acute angle. Thanks! We're glad this was helpful. Thank you for your feedback. If wikiHow has helped you, please consider a small contribution to support us in helping more readers like you. We’re committed to providing the world with free how-to resources, and even $1 helps us in our mission. Support wikiHow Yes No Not Helpful 9 Helpful 11
  • Question How do I use a protractor that doesn't have a hole? Donagan Donagan Top Answerer Use the outside, curved edge. Thanks! We're glad this was helpful. Thank you for your feedback. If wikiHow has helped you, please consider a small contribution to support us in helping more readers like you. We’re committed to providing the world with free how-to resources, and even $1 helps us in our mission. Support wikiHow Yes No Not Helpful 13 Helpful 7
  • Question What about the angle that we want to make in the circle? Donagan Donagan Top Answerer If you're referring to a central angle, draw a diameter. Line up the bottom of the protractor with the diameter so that the midpoint of the protractor aligns with the center of the circle. Use the protractor to draw any central angle up to 180°, using another diameter (or radius) to complete the angle. Thanks! We're glad this was helpful. Thank you for your feedback. If wikiHow has helped you, please consider a small contribution to support us in helping more readers like you. We’re committed to providing the world with free how-to resources, and even $1 helps us in our mission. Support wikiHow Yes No Not Helpful 5 Helpful 9
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Video

Tips

  • An acute angle is an angle from 0 to 89 degrees, which is less than a right angle.[14] Thanks Helpful 0 Not Helpful 0
  • An obtuse angle is an angle greater than a right angle, but less than a straight angle. It can be anything ranging from 91 degrees to 179 degrees.[15] Thanks Helpful 0 Not Helpful 0
  • A straight angle measures to 180 degrees.[16] Thanks Helpful 0 Not Helpful 1
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Expert Interview

Thanks for reading our article! If you’d like to learn more about mathematics, check out our in-depth interview with Taylor Klein.

References

  1. ↑ https://www.mathdoubts.com/protractor/
  2. ↑ https://www.mathdoubts.com/protractor/
  3. ↑ https://www.mathsisfun.com/geometry/protractor-using.html
  4. ↑ https://www.mathopenref.com/angleright.html
  5. ↑ https://www.bbc.co.uk/bitesize/articles/z29kg7h
  6. ↑ https://www.mathsisfun.com/acute.html
  7. ↑ Taylor Klein. Advanced Math Teacher. Expert Interview
  8. ↑ https://www.mathsisfun.com/obtuse.html
  9. ↑ Taylor Klein. Advanced Math Teacher. Expert Interview
More References (7)
  1. ↑ Taylor Klein. Advanced Math Teacher. Expert Interview
  2. ↑ https://www.cuemath.com/geometry/protractor/
  3. ↑ https://www.mathopenref.com/constdrawangle.html
  4. ↑ https://www.cuemath.com/geometry/protractor/
  5. ↑ Taylor Klein. Advanced Math Teacher. Expert Interview
  6. ↑ Taylor Klein. Advanced Math Teacher. Expert Interview
  7. ↑ https://www.bbc.co.uk/bitesize/articles/z29kg7h

About This Article

Taylor Klein Reviewed by: Taylor Klein Advanced Math Teacher This article was reviewed by Taylor Klein. Taylor Klein is an Advanced Math Teacher based in Philadelphia, Pennsylvania. She has worked in the education field for over 10 years, including eight years as a middle school Advanced Math Teacher. She has a master’s degree in Instructional Technology and Design and a master’s degree in Educational Leadership and Administration. This article has been viewed 78,225 times. 10 votes - 54% Co-authors: 13 Updated: July 13, 2025 Views: 78,225 Categories: Geometry
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Yes No Advertisement Cookies make wikiHow better. By continuing to use our site, you agree to our cookie policy. Taylor Klein Reviewed by: Taylor Klein Advanced Math Teacher 10 votes - 54% Click a star to vote Co-authors: 13 Updated: July 13, 2025 Views: 78,225 Thabiso David

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