The arc must be drawn in the interior of the angle to ensure that the angle is big enough to be bisected and that the two arcs intersect.
In addition to the two main reasons listed above, there is also a third reason why the arc is typically drawn in the interior of the angle:
To make the construction easier. It is easier to draw an arc in the interior of an angle than it is to draw an arc on the exterior of an angle. This is because the compass point is less likely to slip off of the paper when drawing an arc in the interior of an angle.
Overall, there are several good reasons why the arc is typically drawn in the interior of the angle when bisecting an angle.
The image shows a question about angle bisectors. The question asks why the arc must be drawn in the interior of the angle.
There are two main reasons why the arc must be drawn in the interior of the angle:
To ensure that the angle is big enough to be bisected. If the arc is drawn on the exterior of the angle, it may not be possible to find a point on the bisecting ray that is also on the arc. This is because the bisecting ray may intersect the arc at a point that is outside of the angle.
To ensure that the two arcs intersect. The two arcs are used to find a point on the bisecting ray. If the arcs do not intersect, then it will not be possible to find a point on the bisecting ray.
In the image, the arc is drawn in the interior of the angle. The two arcs intersect at point D, which is on the bisecting ray of angle A.