LEARN MATH STEP BY STEP THROUGH VERY EASY PROCESS

CONSTRACTION 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:**

__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.__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.__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.__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.__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.__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.