Theory:

What do we do if we need an copy of an already existing angle?
 
Angles of unknown measurements can be copied using compasses.
 
Let us see how to copy an angle of unknown measure.
Copying an angle of unknown measure
Step \(1\): Draw a line on an empty sheet of paper.
 
measure_1_1.png
 
Step \(2\): Consider the already existing angle formed by joining two different lines.
 
fig_14.png
 
Step \(3\): With \(A\) as centre, draw an arc such that the arc cuts both the lines at \(B\) and \(C\).
 
fig_15.png
 
Step \(4\): Keeping the measurements of the arc drawn intact, place a point \(P\) on the line and with \(P\) as centre construct an arc such that the arc meets the line at \(Q\).
 
draw_7.png
 
Step \(5\): Similarly, after measuring the distance between \(B\) and \(C\) using a compass, with \(Q\) as centre place the point \(R\) on the arc.
 
draw_8.png
 
Step \(6\): Join the points \(P\) and \(R\) to form the copied angle.
 
draw_9.png