How to Construct a 30 Degrees Angle Using Compass and Straightedge

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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

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    Let A be the vertex of the angle we're going to construct. [2]
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    Let's call this arc as Arc One . Retain this width of the compass for the remaining steps. [3]
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    [4]
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    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.
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    [5]
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Method 2
Method 2 of 2:

a 60 Degree Angle

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    Construct a 60 o angle as described [7] here .
  2. Bisect the 60 o angle as described here . [8]
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  • 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.
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    Not Helpful 11 Helpful 25
  • Question
    How to construct 15 degree angle?
    Donagan
    Top Answerer
    Construct a 30° angle and bisect it.
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  • 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.
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      Things You'll Need

      • Paper
      • Pen or Pencil
      • Compass
      • Straightedge

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      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!

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        Apr 8, 2020

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