To construct the bisector of ∠A (angle at point A) from the given diagram, follow these steps:

1. Place the compass at point A, and draw an arc that intersects both rays $\overrightarrow{AB}$ and $\overrightarrow{AC}$ at two points. Let these intersection points be called $P$ (on $\overrightarrow{AB}$) and $Q$ (on $\overrightarrow{AC}$).

2. From points P and Q, use the same compass width and draw two arcs that intersect each other. The intersection of these arcs will be a point that lies on the bisector of the angle.

3. Draw a ray from point A through the intersection point of the arcs. This ray is the angle bisector of $\angle A$.

This process will result in a ray that divides the angle $\angle A$ into two equal parts.

Would you like me to break down any of the steps or provide further details?

Here are 5 related questions to deepen your understanding:

1. How can we verify that the constructed bisector divides the angle equally?
2. What is the difference between bisecting an angle and bisecting a line segment?
3. Can an angle bisector be constructed using only a ruler, without a compass?
4. How does an angle bisector relate to the incenter of a triangle?
5. What is the significance of congruent angles when constructing bisectors?

Tip: When using a compass for construction, always keep the compass width consistent between steps to ensure accuracy in the intersection points.