Construction Of Angles

Constructing angles like 60°, 30°, 120°, 90°, 45°, etc. without the use of a protector is an essential part of geometry. Constructing such angles is important in maths as this knowledge is extended for construction of other geometric figures as well, primarily the triangles. In this article, we will discuss constructing angles of measures 60 degrees and 120 degrees. Using these you will also learn the 30 degrees, 90 degree and 45-degree angle constructions using the geometric tools- a compass and a ruler.

Before talking about constructing angles, let us quickly recall the different types of angles in maths, especially in geometry. Depending on the inclination between the two arms, an angle may be acute (less than 90 degrees, say 60 degree angle), obtuse (more than 90 degrees) or right-angled (exactly 90 degrees).

Steps for Angles Construction

60-degree Angle (60°) Construction

60 degree is one of the most basic constructions, which facilitates constructing angles of several other measures. The steps are:

  • Step 1: Draw a line segment. Mark the left end as point O and the right end as point B.

Constructing 60 Degree Angle: Step 1

  • Step 2: Take the compass and open it up to a convenient radius. Place its pointer at O and with the pencil-head make an arc which meets the line OB at say, P.

Constructing 60 Degree Angle: Step 2

  • Step 3: Place the compass pointer at P and mark an arc that passes through O and intersects the previous arc at a point, say A.

Constructing 60 Degree Angle: Step 3

  • Step 4: Draw a line from O through A.

Angles - Construction Of Special Angles

We get the required angle i.e. ∠AOB = 60-degree angle.

30-degree Angle (30°) Construction

A 30-degree angle is the half of 60-degree angle. For its construction, you first construct a 60-degree angle as discussed above. Then, you bisect this angle. You get two 30 degree angles.

120-degree Angle (120°) Construction

A 120-degree angle is the double of a 60-degree angle. The steps for its construction are:

  • Step 1: Draw a line segment. Mark the left end as point O and the right end as point B.

Constructing 120 Degree Angle: Step 1

  • Step 2: Take the compass and open it up to a convenient radius. Place its pointer at O and with the pencil-head make an arc which meets the line OB at say, P.

Constructing 120 Degree Angle: Step 2

  • Step 3: Without disturbing the radius, place the pointer at P and make an arc that cuts the previous arc at a point, say Q.

Constructing 120 Degree Angle: Step 3

  • Step 4: Similarly, with the same radius on the compass, place the pointer at point Q. Mark another arc on the first arc. Mark the point where they intersect as A.

Constructing 120 Degree Angle: Step 4

  • Step 5: Draw a line from O through A.

Constructing 120 Degree Angle: Step 5

We get the required angle, ∠AOB = 120 degrees.

90-degree Angle (90°)

A 90-degree angle lies exactly halfway between a 120-degree angle and a 60 degree angle on a 360 degree scale. For its construction, you first construct a 60° angle and a 120° angle as discussed above. Then, construct an angle bisector between these two angles. Now, you get the required 90 degree angle.

45-degree Angle (45°) Construction

A 45 degree angle is the half of 90° angle. For its construction, you first construct a 90-degree angle as discussed above. Then, you bisect this angle. You get two 45 degree angles.

Note: For constructing angles like 15 degrees or 22.5 degrees, you further bisect 30 degree angle and 45 degree angle respectively.

Check this Video on Angle bisectors:


From the above discussion, one would be able to understand the importance of special angles in the field of geometry. Know further about special angles by solving sample question and answers and to model questions. Also, get class 11 NCERT Solutions for Construction to clear any doubts easily.

To learn more about constructing angles of different measures, download BYJU’S- The Learning App.

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