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How to Construct a 30 Degrees Angle Using Compass and Straightedge Download Article Reviewed by Grace Imson, MA
Last Updated: February 24, 2025 References
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Starting with a Ray
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a 60 Degree Angle
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This article was reviewed by Grace Imson, MA. Grace Imson is a math teacher with over 40 years of teaching experience. Grace is currently a math instructor at the City College of San Francisco and was previously in the Math Department at Saint Louis University. She has taught math at the elementary, middle, high school, and college levels. She has an MA in Education, specializing in Administration and Supervision from Saint Louis University. There are 7 references cited in this article, which can be found at the bottom of the page. This article has been viewed 249,356 times.
Learn to construct a 30o angle using compass and straightedge by different methods.[1]XResearch source
Steps
Method 1 Method 1 of 2:
Starting with a Ray
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1 Draw a ray AB. Let A be the vertex of the angle we're going to construct.[2]XResearch source
2 Place the tip of the compass on A and draw an arc which cuts AB at some point (say X). Let's call this arc as Arc One. Retain this width of the compass for the remaining steps.[3]XResearch source Advertisement
3 Place the tip of the compass on X and draw another arc (call it Arc Two) which cuts Arc One at some point (say Y).[4]XResearch source
4 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 Connect the points A and Z with a straight line and extend it to form a ray AC.[5]XResearch source
The measure of the angle CAB is 30o. Erase any extraneous constructions if you so wish.[6]XResearch source
Advertisement Method 2 Method 2 of 2:
a 60 Degree Angle
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1 Construct a 60o angle as described [7]XResearch source here.
2 Bisect the 60o angle as described here.[8]XResearch source
Upon bisection, you'll have two angles measuring 30o each.
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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. 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 28
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 30 Helpful 76
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 35
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Reviewed by: Grace Imson, MA Math Teacher This article was reviewed by Grace Imson, MA. Grace Imson is a math teacher with over 40 years of teaching experience. Grace is currently a math instructor at the City College of San Francisco and was previously in the Math Department at Saint Louis University. She has taught math at the elementary, middle, high school, and college levels. She has an MA in Education, specializing in Administration and Supervision from Saint Louis University. This article has been viewed 249,356 times. 371 votes - 75% Co-authors: 7Updated: February 24, 2025 Views: 249,356 Categories: Compass ConstructionsArticle SummaryX
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?YesNo
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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 accurate. This works perfectly! Thanks."..." more
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Yes No Advertisement Cookies make wikiHow better. By continuing to use our site, you agree to our cookie policy. Reviewed by: Grace Imson, MA Math Teacher 371 votes - 75% Click a star to vote Co-authors: 7Updated: February 24, 2025 Views: 249,356
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 accurate. This works perfectly! Thanks."..." more
Abha Dixit
Jan 27, 2019
"Your article is extremely helpful and to the point. It helped me a lot! "
Temiloluwa Ade
Jun 16, 2021
"This website really helped me, especially on construction."
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Dec 18, 2016
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Reviewed by: Grace Imson, MA Math Teacher This article was reviewed by Grace Imson, MA. Grace Imson is a math teacher with over 40 years of teaching experience. Grace is currently a math instructor at the City College of San Francisco and was previously in the Math Department at Saint Louis University. She has taught math at the elementary, middle, high school, and college levels. She has an MA in Education, specializing in Administration and Supervision from Saint Louis University. This article has been viewed 249,356 times. 371 votes - 75% Co-authors: 7 Updated: February 24, 2025 Views: 249,356 Categories: Compass Constructions Article SummaryX
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1 Draw a ray AB. Let A be the vertex of the angle we're going to construct.[2] 
2 Place the tip of the compass on A and draw an arc which cuts AB at some point (say X). Let's call this arc as Arc One. Retain this width of the compass for the remaining steps.[3] Advertisement 
3 Place the tip of the compass on X and draw another arc (call it Arc Two) which cuts Arc One at some point (say Y).[4] 
4 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 Connect the points A and Z with a straight line and extend it to form a ray AC.[5] 
1 Construct a 60o angle as described [7] here. 
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 28 
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