Question

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

Explanation:

Step1: Set Compass on Vertex

Place the compass tip at the vertex of the angle. Draw an arc that intersects both sides of the angle. Let the intersection points be \( A \) (on one side) and \( B \) (on the other side).

Step2: Arc from Intersection \( A \)

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

Step3: Arc from Intersection \( B \)

Without changing the compass width, place the compass tip at \( B \) and draw another arc inside the angle. These two arcs should intersect at a point, say \( C \).

Step4: Draw Bisector

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

Answer:

The angle bisector is constructed by following the steps of arc - drawing and line - drawing as described above. (Note: Since this is a construction problem, the final answer is the constructed angle bisector. The steps outline how to achieve it using a compass and ruler.)