When a triangle is translated using a rule such as $(x + 2, y - 1)$, the shape, size, and angles of the triangle do not change. Translation only shifts the position of the triangle on the coordinate plane without altering its internal properties.

Given that angle $A$ of triangle $ABC$ measures 60 degrees, the corresponding angle $A'$ in triangle $A'B'C'$ will also measure 60 degrees.

Therefore, the measure of angle $A'$ is 60 degrees.

Would you like more details or have any questions?

Here are five related questions:

1. How does translation affect the coordinates of a triangle's vertices?
2. What are other types of transformations that can change the angles of a triangle?
3. How does the concept of congruence apply to translated figures?
4. Can translations ever result in different shapes or sizes? Why or why not?
5. How would you determine the coordinates of the new triangle $A'B'C'$ after translation?

Tip: When a figure is translated, remember that all properties like angle measures and side lengths remain unchanged.