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60 Degree Angle – Definition & Construction

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An angle of 60 degrees is an angle that covers one-sixth of a circular area. It is an acute angle meaning that it is less than 90 degrees. The 60-degree angle can very easily be constructed by using a protractor as shown in the below image. It is also the easiest angle to draw using a ruler and compass (without using a protractor).

60 degree angle occupies one sixth of the area of a circle
60 degree angle

How to Construct 60 degree angle:

Step 1: Draw a straight line and draw a point A. The point A will be the vertex of our angle.

Constructing 60 degree angle Step 1

Step 2: Keeping the compass needle at point A we draw a circular arc as shown below.

Constructing 60 degree angle Step 2

Step 3: The circular arc meets the given line at some point label that point as B.

Constructing 60 degree angle Step 3

Step 4: Now keep the compass needle at the point B and draw another circular arc. The two arcs intersect at a point. Label that point as point C.

Constructing 60 degree angle Step 4

Step 5: Join the points A and C giving an angle of 60 degrees. The angle BAC in the below image is 60 degrees.

Constructing 60 degree angle Step 5

Remarks:

  1. In an equilateral triangle, all the angles of the triangle are equal to 60 degrees.
  2. A straight line is an angle of 180 degrees. This means that an angle of 60 degrees occupies one-third of the area of a straight line.
  3. The angle of 30 degrees can be constructed by bisecting the angle of 60 degrees.
  4. The 60 degree is the most elementary construction using ruler and compass. The other angles can be constructed by using the 60 degree angle as the foundation.

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