How to Construct a 30 Degrees Angle Using Compass and Straightedge

Download Article

Reviewed by Grace Imson, MA

Last Updated: November 18, 2022 Fact Checked

Download Article

Learn to construct a 30^o angle using compass and straightedge by different methods.^{[1]
X
Research source}

Method 1

Method 1 of 2:

Starting with a Ray

Download Article

Let A be the vertex of the angle we're going to construct.^{[2]
X
Research source}
Let's call this arc as Arc One. Retain this width of the compass for the remaining steps.^{[3]
X
Research source}

Advertisement
^{[4]
X
Research source}
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]
X
Research source}
- The measure of the angle CAB is 30^o. Erase any extraneous constructions if you so wish.^{[6]
  X
  Research source}

Method 2

Method 2 of 2:

a 60 Degree Angle

Download Article

Construct a 60^o angle as described ^{[7]
X
Research source}here.
2
Bisect the 60^o angle as described here.^{[8]
X
Research source}
- Upon bisection, you'll have two angles measuring 30^o each.

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 26
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