This problem asks to construct angles (marked at points $A$ and $B$) using only a compass and an unmarked ruler. Here's how you can approach constructing angles like those in the image:

Step-by-Step Instructions:

1. Draw a base line:

   • Using the ruler, draw a straight line segment. Label one end as $A$ (or $B$).

2. Mark an arbitrary point above the line:

   • Place the compass point on $A$ (or $B$) and draw an arc above the line.
   • Where the arc intersects the base line is the first reference point.

3. Use the compass to measure and transfer distances:

   • With the same compass opening, place the compass on the reference point and mark an arc. This method ensures you divide the angle consistently.

4. Repeat the process for symmetric points:

   • For both diagrams (a and b), align points to form straight segments meeting at $A$ or $B$. Adjust with the compass to ensure symmetry.

5. Connect the segments:

   • Use the ruler to connect the new points created by the compass arcs. The resulting angles at $A$ and $B$ will be constructed using only the compass and ruler.

Would you like me to provide a detailed geometric construction diagram or clarify any steps?

Related Questions:

1. How do you construct a perpendicular line using only a compass and ruler?
2. What is the process for copying an angle from one location to another?
3. How can you construct an angle bisector with a compass and ruler?
4. How do you construct a 90-degree angle using only basic tools?
5. How do you ensure angles are equal without measuring them numerically?

Tip: Practicing compass constructions helps develop precision and understanding of geometric relationships.