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Constructing 6060 angle using Compass


    what you'll learn...

overview

In this page, constructing the following using a compass are explained.

 • 6060 angle

 • 3030 angle

 • 120120 angle

 • 1515 angle

 • 9090 angle

Constructing 60 angle using Compass

We know that, Angles in a equilateral triangle are 60. This geometrical property helps to construct 60 angle using a compass.

construct 60 degree

To construct an angle measuring 60 at point A on line ¯AB, construct a equilateral triangle as given below.

 •  With an arbitrary distance measure on compass, mark point P from point A on line ¯AB.

 •  With the same distance measure on compass, construct two arcs from points A and P. The arcs cut at point Q.

Since the distance measure on compass is identical, points A, P, and Q make an equilateral triangle. The line ¯AQ is extended and PAQ is 60

Constructing 60 angle using a Compass : Construct an equilateral triangle and the angle 60 is constructed at the vertex.

Constructing 30 angle using Compass

To construct 30 angle using a compass, we use the property that 30 is half of 60.

construct 30 degree

We have learned constructing 60 and bisecting an angle using a compass. Combine these two to construct 30 angle.

 •  With an arbitrary distance-measure on compass, mark point P from point A on line ¯AB.

 •  With the same distance measure on compass, construct two arcs from points A and P. The arcs cut at point Q. ¯AQ makes 60 with the ¯AP.

 •  With an arbitrary distance-measure on compass, construct two arcs from points P and Q. These arcs cut at point R. The line ¯AR bisects the angle PAQ.

The angle 30 is constructed as PAR.

Constructing 30 angle using a Compass : Construct an equilateral triangle and the angle 60 is constructed at the vertex. Bisect the angle.

Constructing 120 angle using Compass

To construct 120 angle using a compass, we use the property that 120 is double of 60.

construct 120 degree

Constructing 60 angle twice-over to construct 120

 •  With an arbitrary distance-measure on compass, mark point P from point A on line ¯AB.

 •  With the same distance measure on compass, construct two arcs from points A and P. The arcs cut at point Q. ¯AQ makes 60 with the ¯AP.

 •  With the same distance measure on compass, construct two arcs from points A and Q. The arcs cut at point R. ¯AR makes 120 with the ¯AP. The angle 120 is constructed as PAR.

Constructing 120 angle using a Compass : Construct an equilateral triangle and another equilateral triangle on the side of the constructed one.

Constructing 15 angle using Compass

To construct 15 angle using a compass, we use the property that 15 is half of 30.

construct 15 degree

We have learned constructing 60 and bisecting an angle using a compass. Combine these two to construct 15 angle.

 •  With an arbitrary distance-measure on compass, mark point P from point A on line ¯AB.

 •  With the same distance measure on compass, construct two arcs from points A and P. The arcs cut at point Q. ¯AQ makes 60 with the ¯AP.

 •  With an arbitrary distance-measure on compass, construct two arcs from points P and Q. These arcs cut at point R. The line ¯AR bisects the angle PAQ.

 •  With an arbitrary distance-measure on compass, construct two arcs from points P and R. These arcs cut at point S. The line ¯AS bisects the angle PAS.

The angle 15 is constructed as PAS.

Constructing 15 angle using a Compass : Construct an equilateral triangle and the angle 60 is constructed at the vertex. Bisect the angle twice.

Constructing 90 angle using Compass

To construct 90 angle using a compass, we use the property that 90 is sum of 60 and 30.

construting 90 degree using a compass

Constructing 90 with two 60 is illustrated

 •  With an arbitrary distance-measure on compass, mark point P from point A on line ¯AB.

 •  With the same distance measure on compass, construct two arcs from points A and P. The arcs cut at point Q. ¯AQ makes 60 with the ¯AP.

 •  With the same distance measure on compass, construct two arcs from points A and Q. The arcs cut at point R. ¯AR makes 120 with the ¯AP.

 •  With an arbitrary distance-measure on compass, construct two arcs from points Q and R. These arcs cut at point S. The line ¯AS bisects the angle QAR.

The angle 90 is constructed as PAS.

Constructing 90 angle using a compass : Construct two equilateral triangles and bisect the second one to construct 90 angle.

summary

Constructing 60 angle using a Compass : Construct an equilateral triangle and the angle 60 is constructed at the vertex.

Constructing 30 angle using a Compass : Construct an equilateral triangle and the angle 60 is constructed at the vertex. Bisect the angle.

Constructing 120 angle using a Compass : Construct an equilateral triangle and another equilateral triangle on the side of the constructed one.

Constructing 15 angle using a Compass : Construct an equilateral triangle and the angle 60 is constructed at the vertex. Bisect the angle twice.

Constructing 90 angle using a compass : Construct two equilateral triangles and bisect the second one to construct 90 angle.

Outline

The outline of material to learn "Construction / Practical Geometry at 6-8th Grade level" is as follows. Note: click here for detailed outline of "constructions / practical geometry".

  •   Four Fundamenatl elements

    →   Geometrical Instruments

    →   Practical Geometry Fundamentals

  •   Basic Shapes

    →   Copying Line and Circle

  •   Basic Consustruction

    →   Construction of Perpendicular Bisector

    →   Construction of Standard Angles

    →   Construction of Triangles

  •   Quadrilateral Forms

    →   Understanding Quadrilaterals

    →   Construction of Quadrilaterals

    →   Construction of Parallelograms

    →   Construction of Rhombus

    →   Construction of Trapezium

    →   Construction of Kite

    →   Construction of Rectangle

    →   Construction of Square