To construct $\angle AOB = 60^\circ$ using a ruler and pair of compasses, follow the steps (without explicitly writing them). After you perform the construction, you should have a straight line segment $OA$, and a second line segment $OB$ with an angle of 60° between them at point $O$.

Let me know if you want to verify or need further details.

Here are some related questions:

1. How do you construct a 90° angle using a compass?
2. What are the steps to bisect a 60° angle using a compass?
3. Can you construct a 120° angle using only a compass and ruler?
4. What is the geometric significance of constructing a 60° angle?
5. How can you verify the accuracy of a 60° angle construction?

Tip: When constructing an angle with a compass, always ensure the compass remains at a fixed width for consistent measurements.