CLASS-6
CONSTRACTION OF 120-DEGREE ANGLE

CONSTRACTION OF 120-DEGREE (120º) ANGLE -

To construct a 120-degree angle, you can follow these steps using a compass and a straightedge:

  1. Draw a Ray:- Start by drawing a ray (a straight line that extends indefinitely in one direction) using a straightedge. This ray will be the initial side of the angle.
  2. Place the Compass:- Place the compass on one endpoint of the ray, and open it to a convenient width. This width will be used to mark points on the ray.
  3. Draw an Arc:- With the compass set at the initial endpoint, draw an arc that intersects the ray. Let's call this point of intersection A.
  4. Without Changing the Compass Width:- Without changing the compass width, place the compass on point A and draw another arc that intersects the first arc. Let's call this point of intersection B.
  5. Draw Another Arc:- Without changing the compass width, place the compass on point B and draw another arc that intersects the first arc. Let's call this point of intersection C.
  6. Draw the Angle:- Use a straightedge to draw lines connecting the initial endpoint of the ray to points A, B, and C. The angle formed by the initial ray and the lines connecting the three points is a 120-degree angle.

This construction works based on the properties of equilateral triangles. If you construct an equilateral triangle (a triangle with all sides equal), each angle will be 60 degrees. By extending the sides of an equilateral triangle, you can create a 120-degree angle at the vertex.

Please note that this method relies on extending the sides of an equilateral triangle, and it assumes you are familiar with constructing equilateral triangles.


Another Way Of Understanding -

Step 1:- Draw any ray OA.

Step 2:- With O as centre and any (suitable) radius, draw an arc to meet the ray OA at C.

Graphs

Step 3:- With C as centre and same radius (as in Step .2), draw an arc to meet the previous arc at D.

Step 4:- With D as centre and same radius, draw another arc to meet the first arc at E.

Step 5:- Join OE and produce it to form ray OB, then ∠AOB = 120º