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In these lessons, we will learn how to construct a 30-degree angle from a 60-degree angle.

Related Pages

Constructing Angles

Construct 45° Angles

More Geometry Lessons

We can use the angle bisector method to construct some other angles from existing angles.

Examples:

A 30° angle can be obtained by bisecting a 60° angle.

A 15° angle can be obtained by bisecting a 30° angle.

A 45° angle can be obtained by bisecting a 90° angle.

A 22.5° angle can be obtained by bisecting a 45° angle.

Example:

The figure shows a point B on a straight line. Construct an angle of 30° at point B.

Solution:

Construct a 60° angle, and then construct an angle bisector to obtain a 30° angle.

Step 1: Stretch the compasses to any width. Put the sharp end of the compasses at point B and draw an arc on the line. Label the point where the arc intersects the line as point C.

Step 2: While keeping the sharp end of the compasses at point B, move the compasses away from C and draw a second arc above the line about mid-way between points B and C.

Step 3: Without changing the width of the compasses, place the sharp end of the compasses at point C and draw an arc to intersect the second arc.

Step 4: Draw a line from point B to the point of intersection of the 2 arcs. Angle ABC is 60˚.

Step 5: We now need to Bisect angle ABC. Put the sharp end of your compasses at point B and make one arc on the line BC (point S) and another arc on line AB (point T).

Step 6: Without changing the width of your compasses, put the sharp end of the compasses at S and make an arc within the lines AB and BC. Do the same at T and make sure that the second arc intersects the first arc.

Step 7: Draw a line from point B to the points of intersection

of the 2 arcs. This line MB bisects .

Angle MBC is 30 degrees.

How To Construct A 45 Degree Angle Using A Compass And Ruler

Constructing a 45-degree angle can be done by first constructing a 90-degree angle and then bisecting this 90-degree angle. Make sure you know how to construct an angle bisector and a 90-degree angle before you attempt constructing a 45-degree angle.

How to construct a 30 degree angle using a pencil, ruler and a pair of compasses only?

How to construct an angle of 30 and 60 degrees?

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