Theory:

The angle bisector is formed when a line or line segment divides an angle into two equal parts.
pic 13 (1).svg
 
pic 14 (2).svg
 
Follow the below steps, construct the bisector of the \(∠ABC\) with the measure \(60°\).
 
Step 1: Draw the given angle \(∠ABC\) with the measure \(60°\) using the protractor.
 
pic 15 (1).svg
 
Step 2: Taking \(A\) as centre and convenient radius, draw an arc to cut \(AB\) and \(AC\). Mark the points of intersection as \(E\) on \(AB\) and \(F\) on \(AC\).
 
pic 16 (1).svg
 
With the same radius and \(E\) as centre, draw an arc in the interior of \(∠CAB\) and another arc of same measure with centre at \(F\) to cut the previous arc.
 
\(AG\) is the required bisector of the given angle \(∠CAB\).
 
pic 17 (1).svg
 
Mark the point of intersection as \(G\). Draw a ray \(AX\) through \(G\).