How to Construct a 30 Degrees Angle Using Compass and Straightedge

PDF download Download Article
PDF download Download Article

Learn to construct a 30 o angle using compass and straightedge by different methods. [1]

Method 1
Method 1 of 2:

Starting with a Ray

PDF download Download Article
  1. {"smallUrl":"https:\/\/www.wikihow.com\/images\/thumb\/0\/03\/Construct-a-30-Degrees-Angle-Using-Compass-and-Straightedge-Step-1.jpg\/v4-460px-Construct-a-30-Degrees-Angle-Using-Compass-and-Straightedge-Step-1.jpg","bigUrl":"\/images\/thumb\/0\/03\/Construct-a-30-Degrees-Angle-Using-Compass-and-Straightedge-Step-1.jpg\/aid3263930-v4-728px-Construct-a-30-Degrees-Angle-Using-Compass-and-Straightedge-Step-1.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><p>License: <a target=\"_blank\" rel=\"nofollow noreferrer noopener\" class=\"external text\" href=\"https:\/\/creativecommons.org\/licenses\/by-nc-sa\/3.0\/\">Creative Commons<\/a><br>\n<\/p><p><br \/>\n<\/p><\/div>"}
    Let A be the vertex of the angle we're going to construct. [2]
  2. {"smallUrl":"https:\/\/www.wikihow.com\/images\/thumb\/2\/2b\/Construct-a-30-Degrees-Angle-Using-Compass-and-Straightedge-Step-2.jpg\/v4-460px-Construct-a-30-Degrees-Angle-Using-Compass-and-Straightedge-Step-2.jpg","bigUrl":"\/images\/thumb\/2\/2b\/Construct-a-30-Degrees-Angle-Using-Compass-and-Straightedge-Step-2.jpg\/aid3263930-v4-728px-Construct-a-30-Degrees-Angle-Using-Compass-and-Straightedge-Step-2.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><p>License: <a target=\"_blank\" rel=\"nofollow noreferrer noopener\" class=\"external text\" href=\"https:\/\/creativecommons.org\/licenses\/by-nc-sa\/3.0\/\">Creative Commons<\/a><br>\n<\/p><p><br \/>\n<\/p><\/div>"}
    Let's call this arc as Arc One . Retain this width of the compass for the remaining steps. [3]
    Advertisement
  3. {"smallUrl":"https:\/\/www.wikihow.com\/images\/thumb\/5\/56\/Construct-a-30-Degrees-Angle-Using-Compass-and-Straightedge-Step-3.jpg\/v4-460px-Construct-a-30-Degrees-Angle-Using-Compass-and-Straightedge-Step-3.jpg","bigUrl":"\/images\/thumb\/5\/56\/Construct-a-30-Degrees-Angle-Using-Compass-and-Straightedge-Step-3.jpg\/aid3263930-v4-728px-Construct-a-30-Degrees-Angle-Using-Compass-and-Straightedge-Step-3.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><p>License: <a target=\"_blank\" rel=\"nofollow noreferrer noopener\" class=\"external text\" href=\"https:\/\/creativecommons.org\/licenses\/by-nc-sa\/3.0\/\">Creative Commons<\/a><br>\n<\/p><p><br \/>\n<\/p><\/div>"}
    [4]
  4. {"smallUrl":"https:\/\/www.wikihow.com\/images\/thumb\/f\/f3\/Construct-a-30-Degrees-Angle-Using-Compass-and-Straightedge-Step-4.jpg\/v4-460px-Construct-a-30-Degrees-Angle-Using-Compass-and-Straightedge-Step-4.jpg","bigUrl":"\/images\/thumb\/f\/f3\/Construct-a-30-Degrees-Angle-Using-Compass-and-Straightedge-Step-4.jpg\/aid3263930-v4-728px-Construct-a-30-Degrees-Angle-Using-Compass-and-Straightedge-Step-4.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><p>License: <a target=\"_blank\" rel=\"nofollow noreferrer noopener\" class=\"external text\" href=\"https:\/\/creativecommons.org\/licenses\/by-nc-sa\/3.0\/\">Creative Commons<\/a><br>\n<\/p><p><br \/>\n<\/p><\/div>"}
    Place the tip of the compass on Y and draw another arc ( Arc Three ) so as to cut Arc Two at a point (say Z) which is on that side of Arc Two which does not contain the point A.
  5. {"smallUrl":"https:\/\/www.wikihow.com\/images\/thumb\/3\/35\/Construct-a-30-Degrees-Angle-Using-Compass-and-Straightedge-Step-5.jpg\/v4-460px-Construct-a-30-Degrees-Angle-Using-Compass-and-Straightedge-Step-5.jpg","bigUrl":"\/images\/thumb\/3\/35\/Construct-a-30-Degrees-Angle-Using-Compass-and-Straightedge-Step-5.jpg\/aid3263930-v4-728px-Construct-a-30-Degrees-Angle-Using-Compass-and-Straightedge-Step-5.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><p>License: <a target=\"_blank\" rel=\"nofollow noreferrer noopener\" class=\"external text\" href=\"https:\/\/creativecommons.org\/licenses\/by-nc-sa\/3.0\/\">Creative Commons<\/a><br>\n<\/p><p><br \/>\n<\/p><\/div>"}
    [5]
    6. Advertisement
Method 2
Method 2 of 2:

a 60 Degree Angle

PDF download Download Article
  1. {"smallUrl":"https:\/\/www.wikihow.com\/images\/thumb\/3\/38\/Construct-a-30-Degrees-Angle-Using-Compass-and-Straightedge-Step-6.jpg\/v4-460px-Construct-a-30-Degrees-Angle-Using-Compass-and-Straightedge-Step-6.jpg","bigUrl":"\/images\/thumb\/3\/38\/Construct-a-30-Degrees-Angle-Using-Compass-and-Straightedge-Step-6.jpg\/aid3263930-v4-728px-Construct-a-30-Degrees-Angle-Using-Compass-and-Straightedge-Step-6.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><p>License: <a target=\"_blank\" rel=\"nofollow noreferrer noopener\" class=\"external text\" href=\"https:\/\/creativecommons.org\/licenses\/by-nc-sa\/3.0\/\">Creative Commons<\/a><br>\n<\/p><p><br \/>\n<\/p><\/div>"}
    Construct a 60 o angle as described [7] here .
  2. Bisect the 60 o angle as described here . [8]
    3. Advertisement

Community Q&A

Search
Add New Question
  • Question
    Can I construct a 30-degree angle from a 60-degree angle?
    Donagan
    Top Answerer
    Let's assume you want to bisect a 60° angle using a compass and straightedge. Place the point of the compass at the 60° angle's vertex. Strike an arc through the angle at a convenient distance. Label as A and B the points where the arc intersects the angle's two rays. Place the compass point at A, and strike an arc within the angle's rays. Place the compass point at B, and using the same radius, strike another arc within the rays. Label as C the point of intersection of the two arcs. Draw a straight line from the angle's vertex to point C. That line bisects the 60° angle, forming two 30° angles.
    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 11 Helpful 25
  • Question
    How to construct 15 degree angle?
    Donagan
    Top Answerer
    Construct a 30° angle and bisect it.
    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 27 Helpful 75
  • Question
    How do I construct an angle of 60 degrees?
    Donagan
    Top Answerer
    Draw a horizontal line segment of any convenient length. Use a compass to measure the length of the line segment. Put the compass point at one end of the line segment and strike an arc with a radius the length of the line segment. Do the same from the other end of the line segment so that the second arc intersects the first arc. From the intersection of the two arcs, draw straight lines to both ends of the line segment. The triangle thus drawn will consist of three 60-degree angles.
    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 14 Helpful 34
See more answers
Ask a Question
200 characters left
Include your email address to get a message when this question is answered.
Submit
      Advertisement

      Video

      Tips

      Submit a Tip
      All tip submissions are carefully reviewed before being published
      Name
      Please provide your name and last initial
      Submit
      Thanks for submitting a tip for review!

      Things You'll Need

      • Paper
      • Pen or Pencil
      • Compass
      • Straightedge

      You Might Also Like

      How to
      Construct a 60 Degrees Angle Using Compass and Ruler
      How to
      Construct a 90 Degrees Angle Using Compass and Ruler
      How to
      Construct a Regular Pentagon
      How to
      Construct a Line Parallel to a Given Line Through a Given Point
      How to
      Create a Regular Heptagon
      How to
      Bisect a Line With a Compass and Straightedge
      How to
      Construct a Perpendicular Line to a Given Line Through Point on the Line
      How to
      Construct an Angle Congruent to a Given Angle
      Advertisement

      References

      1. ↑ https://www.mathopenref.com/const306090.html
      2. ↑ https://www.mathopenref.com/vertex.html
      3. ↑ https://www.mathopenref.com/constangle30.html
      4. ↑ https://www.mathsteacher.com.au/year8/ch10_geomcons/05_angles/const.htm
      5. ↑ https://www.mathsisfun.com/geometry/construct-30degree.html
      6. ↑ https://www.mathopenref.com/const306090.html
      7. ↑ https://www.mathopenref.com/constangle60.html
      8. ↑ https://www.mathsisfun.com/geometry/construct-60degree.html

      About This Article

      Article Summary X

      To construct a 30-degree angle, you’ll need a compass, a straightedge, such as a ruler, and a pencil. Start by drawing a horizontal line and marking the left end “A” and the right end “B” to serve as the vertex of the angle. Then, place the tip of the compass on “A” and draw an arc through the vertex line. Mark the spot the arc crosses the vertex as “X.” Now place the tip of the compass on “X” and draw a second arc through the first arc. Mark the point they intersect as “Z” To make the 30-degree angle, simply use your ruler to draw a line connecting “A” and “Z.” To learn how to measure out a 60-degree angle, read on!

      Did this summary help you?
      In other languages
      Thanks to all authors for creating a page that has been read 241,664 times.

      Reader Success Stories

      • Jeff Dupre

        Apr 8, 2020

        "I needed a method to draw a 60-degree angle on a construction project that could be scaled up 30 ft and remain ..." more
      More reader stories Hide reader stories
      Share your story

      Did this article help you?

      Advertisement