Q&A for How to Construct a 30 Degrees Angle Using Compass and Straightedge

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.

Construct a 30° angle and bisect it.

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.

First construct a 90° angle. See Construct a 90 Degrees Angle Using Compass and Ruler . Then bisect that angle this way: Strike an arc through both rays of the angle. Label as A and B the points of intersection of the arc and the rays. From A and B strike two arcs of equal radius within the angle. Label as C the point of intersection of the arcs. Draw a straight line from C to the vertex of the 90° angle. That line bisects the 90° angle into two 45° angles.

A compass is useful for angle construction only if you want to construct an angle of 30°, 45°, 60° or 90°. It's not practical for other angles.