Theory:

The angle bisector is formed when a line or line segment divides an angle into two equal parts.
Bi.jpg
 
Bi1.jpg
 
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.
 
Theory1.jpg
 
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 \(AC\).
 
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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 \(∠CAB\).
 
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Mark the point of intersection as \(G\). Draw a ray \(AX\) through \(G\).