# CLASS-6CONSTRUCTION OF ANGLES

CONSTRUCTION OF ANGLES -

Constructing angles involves using a compass and a straightedge (ruler) to create specific angles. Here are the steps for constructing angles:

Constructing an Angle of a Given Measure:-

Materials Needed:-

• Compass
• Straightedge (Ruler)

Steps :-

1. Draw a Ray (Initial Side):- Start by drawing a ray (a straight line that extends in one direction) using the straightedge. This will be one side of your angle, called the initial side.
2. Place the Compass at the Vertex:- Put the pointed end of the compass on the endpoint of the initial side (vertex of the angle).
3. Open the Compass:- Open the compass to a length that is more than half the expected measure of the angle. This will ensure that the arc you draw intersects the initial side.
4. Draw an Arc:- Keeping the compass settings fixed, draw an arc that intersects the initial side. This arc will be the second side of the angle.
5. Draw the Final Side:- Without changing the compass settings, place the compass on the intersection point of the arc and the initial side. Draw another arc that intersects the previous arc.
6. Draw the Angle:- Use the straightedge to draw a line connecting the vertex to the point where the two arcs intersect. This line forms the final side of the angle.

A) Constructing a Specific Angle (e.g., 60 degrees):-

Steps:-

1. Draw a Ray (Initial Side):- Start by drawing a ray using the straightedge. This will be one side of your angle.
2. Place the Compass at the Vertex:- Put the pointed end of the compass on the endpoint of the initial side.
3. Set the Compass to the Desired Angle:- Open the compass to a specific angle measurement (e.g., 60 degrees).
4. Draw an Arc:- Keeping the compass settings fixed, draw an arc that intersects the initial side.
5. Draw the Final Side:- Without changing the compass settings, place the compass on the endpoint of the initial side. Draw another arc that intersects the previous arc.
6. Draw the Angle:- Use the straightedge to draw a line connecting the vertex to the point where the two arcs intersect. This line forms the final side of the angle.

B. Constructing a 90-Degree Angle (Right Angle):-

1. Draw a straight line using a ruler.
2. Place the compass at one end of the line, and draw an arc that intersects the line.
3. Without changing the compass width, place the compass at the intersection point on the line, and draw another arc.
4. The intersection of the two arcs is the right angle (90 degrees).

C. Constructing a 45-Degree Angle:-

1. Draw a straight line using a ruler.
2. Place the compass at one end of the line and draw an arc that intersects the line.
3. Without changing the compass width, place the compass at the other end of the line, and draw another arc.
4. The intersection of the line and the arc is the 90-degree angle.
5. Without changing the compass width, place the compass at the intersection point, and draw an arc above the line.
6. The angle between the original line and the new arc is 45 degrees.

D. Constructing a 30-Degree Angle:-

1. Draw a straight line using a ruler.
2. Place the compass at one end of the line and draw an arc that intersects the line.
3. Without changing the compass width, place the compass at the intersection point on the line, and draw another arc.
4. The intersection of the line and the second arc is the 60-degree angle.
5. Without changing the compass width, place the compass at the intersection point, and draw an arc below the line.
6. The angle between the original line and the new arc is 30 degrees.

These constructions are basic and assume you have a ruler and compass. For more complex constructions involving specific angles or geometric shapes, additional steps and constructions may be necessary.