# CLASS-6CONSTRACTION OF 30-DEGREE ANGLE

CONSTRACTION OF 30-DEGREE ANGLE -

To construct a 30-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 the Angle Bisector:- Use the compass to measure the distance from point A to point B. Without changing the compass width, place the compass on point B, and draw an arc that intersects the arc created in step 3. Let's call this point of intersection C.
6. Connect the Points:- Use a straightedge to draw a line connecting the initial endpoint of the ray to point C (the second intersection point).

The angle formed by the initial ray and the line connecting the two intersection points (A and C) is a 30-degree angle.

This construction works by creating an isosceles triangle (a triangle with two sides of equal length). The angle bisector of the vertex angle (angle between the two equal sides) creates two congruent angles, each measuring 30-degrees.

Another way of Understanding -

Constructing a 30º Angle

We know that:

1/2 of 60º is 30º

So, to construct an angle of 30º, first construct a 60º angle and then bisect it. Often, we apply the following steps.

Step 1:- Draw the arm PQ. compass arc

Step 2:- Place the point of the at P and draw an that passes through Q.

﻿Step 3:-﻿ Place the point of the compass at Q and draw an arc that cuts the arc drawn in Step 2 at R.

﻿﻿Step 4﻿:-﻿ With the point of the compass still at Q, draw an arc near T as shown.

Step 5:- With the point of the compass at R, draw an arc to cut the arc drawn in Step 4 at T.

Step 6:-  Join T to P. The angle QPT is 30º.