Construction of an Angle Bisector

The ray \(BX\) divides the angle \(ABC\) into two equal angles, i.e. angle \(ABX=\) angle \(CBX\).
Thus, \(BX\) bisects angle \(ABC\).
Any point on the angle bisector of an angle is equidistant from the two sides of the angle.
(Ray is a line with a fixed starting point but no end point)

Steps of Drawing Angle Bisector

1. Draw the angle \(ABC\) by using a ruler and a protractor.
2. With \(B\) as centre, use your compass to draw arcs which cut line segments \(AB\) and \(BC\) at \(X\) and \(Y\) respectively.
3. With \(X\) and \(Y\) as centres, use equal compass radii to draw arcs that intersect inside the angle.
4. Connect point \(B\) and where the arcs cross with a ray.