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Learn to construct a 30o angle using compass and straightedge by different methods.[1]
Steps
Draw a ray AB. Let A be the vertex of the angle we're going to construct.[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
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]
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.
Connect the points A and Z with a straight line and extend it to form a ray AC.[5]- The measure of the angle CAB is 30o. Erase any extraneous constructions if you so wish.[6]
- The measure of the angle CAB is 30o. Erase any extraneous constructions if you so wish.[6]
Community Q&A
- QuestionCan I construct a 30-degree angle from a 60-degree angle?
DonaganTop AnswererLet'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. - QuestionHow to construct 15 degree angle?DonaganTop AnswererConstruct a 30° angle and bisect it.
- QuestionHow do I construct an angle of 60 degrees?DonaganTop AnswererDraw 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.
Video
Tips
Things You'll Need
- Paper
- Pen or Pencil
- Compass
- Straightedge
References
- ↑ https://www.mathopenref.com/const306090.html
- ↑ https://www.mathopenref.com/vertex.html
- ↑ https://www.mathopenref.com/constangle30.html
- ↑ https://www.mathsteacher.com.au/year8/ch10_geomcons/05_angles/const.htm
- ↑ https://www.mathsisfun.com/geometry/construct-30degree.html
- ↑ https://www.mathopenref.com/const306090.html
- ↑ https://www.mathopenref.com/constangle60.html
- ↑ https://www.mathsisfun.com/geometry/construct-60degree.html
About This Article
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!
Reader Success Stories
"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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