How to Construct a 60 Degrees Angle Using Compass and Ruler

Last Updated: February 21, 2023

Often you are required to construct some angles without using a protractor. This article teaches you how to draw a 60 degrees angle using a compass and a ruler.

Steps

1
Mark the vertex of your angle anywhere on the paper. Let us name this point as M.^{[1]
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2
Draw a ray MN, extending in any direction and of any length. This will be one of the arms of our angle.^{[2]
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3
Place the tip of the compass on point M and set its width to any measure less than the length of the ray MN.^{[3]
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4
With the tip of the compass still on M, draw an arc so as to cut the ray MN at some point (say P).^{[4]
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5
Keeping the width unchanged, place the tip of the compass on the point P and draw another arc cutting the arc drawn in the previous step at some point (say Q).^{[5]
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6
Connect the points M and Q with a straight line and extend it to form a ray ML.^{[6]
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- The measure of the angle LMN is 60^O.

Community Q&A

Question

What are the steps to construct a 90 degree angle?

Donagan

Top Answerer

Draw a base line. Pick a point on the base line. Mark an equal distance from that point in each direction of the line so that you now have two new points on the base line. Use the compass to strike two arcs of equal radius, one centered on each of the two new points. Draw a line from the original point on the base line to the intersection(s) of the arcs. This new line is perpendicular to the base line and makes two 90-degree angles with it.
Question

How do I construct a 45 degree angle?

Donagan

Top Answerer

Pick a point on a line to be the vertex of your angle. Mark a convenient distance along the line from the vertex. Draw a new line perpendicular to the first line at the point you measured. Measure from that point along the perpendicular line a distance equal to the distance along the first line from the vertex to the base of the perpendicular line. Mark that last measurement. Draw a line from the vertex to that last mark you made. The new line makes a 45-degree angle with the original line.
Question

How can I make 30-degree angle?

Donagan

Top Answerer

Construct a 60° angle as shown above. Then bisect it using a compass and straightedge. You wind up with two 30° angles.