Image of the division of line segment AB in the ratio 3:2 is given below.

$\angle BAX$ is a/an :

A triangle similar to given $\Delta ABC$with sides equal to $\frac{3}{4}$ of the sides of $\Delta ABC$ is to be constructed as the given image. Arrange the following steps of construction in order:
1. Join $B_{4}C$ and raw a line through $B_3$( the third point, 3 being smaller of 4 in$\frac{3}{4}$) parallel to $B_{4}C$  to intersect BC at C'.
2. Draw any ray BX making an acute angle with BC on the side opposite to  the vertex A.
3. Locate 4(the greater of 3 and 4 in$\frac{3}{4}$) points $B_1,B_2,B_3\text{and}{B}_4$ on BX  so that $B{B}_1=B_1{B}_2=B_2{B}_3=B_3{B}_4$
4. Draw a line through C' parallel to the line CA to intersect BA at A'.

A triangle similar to given $\Delta ABC$with sides equal to $\frac{3}{4}$ of the sides of $\Delta ABC$ is constructed.

$\frac{B{C}^{\prime }}{BC}$ is equal to____.

Initial step for constructing a similar triangle of $\Delta ABC$ is given below $\angle CBX$ is a/an:

Construction of a $\Delta A^{\prime }{C}^{\prime }B$ similar to $\Delta ACB$ is shown in the figure below, which condition is used to construct $A^{\prime }{C}^{\prime }$ ||$AC$?

Steps to divide a line segment  AB in the given ratio m : n by drawing alternated angles is given. Choose the correct order.
1.Draw any ray AX making acute angle with AB and  ray BY such that $\angle BAX=\angle ABY$.
2.Locate the points $A_1,A_2,A_3...A_m$ on AX and  $B_1,B_2,B_3...B_n$ on BY such that $A{A}_1=A_1{A}_2=B{B}_1=B_1{B}_2$
3.Draw a ray BY parallel to AX by making $\angle ABY=\angle BAX$
4.Join $A_m{B}_n$.

If a triangle similar to given $\Delta ABC$ with sides equal to $\frac{3}{4}$ of the sides of $\Delta ABC$ is to be constructed, then the number of points to be marked on ray BX is __.

What is the ratio $\frac{AC}{BC}$ for the line segment AB following the construction method below?
Step 1. A ray is extended from A and 30 arcs of equal lengths are cut, cutting the ray at $A_1,A_2,...,A_{30}$
Step 2. A line is drawn from $A_{30}$ to $B$ and a line parallel to $A_{30}B$ is drawn, passing through the point $A_{17}$ and meet AB at C.