The problem asks for the measure of angle $\text{DEF}$ in the triangle $\text{DEF}$, which is a scaled copy of triangle $\text{ABC}$.

In similar triangles, corresponding angles are congruent. Therefore, the angles in triangle $\text{DEF}$ will be identical to the corresponding angles in triangle $\text{ABC}$.

The angles given for triangle $\text{ABC}$ are:

• $\angle A = 42^\circ$
• $\angle B = 60^\circ$
• $\angle C = 78^\circ$

Looking at the diagram:

• $\angle A$ corresponds to $\angle D$
• $\angle B$ corresponds to $\angle E$
• $\angle C$ corresponds to $\angle F$

Since we are looking for $\angle DEF$, which corresponds to $\angle A = 42^\circ$, the measure of $\angle DEF$ is $42^\circ$.

Would you like further details or have any questions?

Here are five related questions to explore further:

1. What are the properties of similar triangles?
2. How can you determine if two triangles are similar?
3. What is the difference between congruent and similar triangles?
4. How do the sides of similar triangles compare?
5. What other geometric transformations preserve angle measures?

Tip: When dealing with similar triangles, always look for corresponding angles, as they will have the same measures.