Question

use the compass and ruler to construct the bisector of the angle below.

Explanation:

Step1: Place compass at vertex

Put the compass point on the angle's vertex (the intersection of the two blue rays). Draw an arc that intersects both sides of the angle. Let's call the intersection points \( A \) (on one ray) and \( B \) (on the other ray).

Step2: Arc from point A

With the same compass width, place the compass point on \( A \) and draw an arc inside the angle.

Step3: Arc from point B

Without changing the compass width, place the compass point on \( B \) and draw another arc inside the angle. This arc should intersect the arc drawn from \( A \); call the intersection point \( C \).

Step4: Draw bisector

Use a ruler to draw a line from the vertex of the angle through point \( C \). This line is the angle bisector.

Answer:

The angle bisector is constructed by following the steps of angle - bisector construction (placing compass at vertex, drawing arcs intersecting sides, then arcs from those intersection points, and drawing a line through the vertex and the intersection of the inner arcs). The final constructed bisector is a line that splits the given angle into two equal - measure angles. (Note: Since this is a construction problem, the answer is the process - constructed bisector as per the steps above. If a visual representation was possible, it would show the bisector line in the angle.)