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To solve this problem, let’s analyze the given information step-by-step.

1. **Similarity of Triangles**:
   The two triangles \( ABC \) and \( EFG \) are similar, which means all corresponding angles are equal, and the sides are proportional.

2. **Given Angle**:
   In triangle \( ABC \), angle \( \angle CAB \) is \( 42^\circ \).

3. **Corresponding Angles**:
   Since the triangles are similar, the angles in triangle \( EFG \) will match the angles in triangle \( ABC \).
   
   - Therefore, \( \angle EFG = \angle ABC \)
   - \( \angle GEF = \angle CAB \)
   - \( \angle FEG = \angle ACB \)

4. **Finding the Measure of Angle**:
   Given that \( \angle CAB = 42^\circ \), the corresponding angle in the right triangle (likely \( \angle GEF \)) is also \( 42^\circ \).

Thus, the measure of angle \( \angle GEF \) in triangle \( EFG \) is \( 42^\circ \).

Would you like further clarification on any step or more details about solving similar triangles?

### Related Questions

1. How do we find other angle measures in similar triangles?
2. What is the proportionality relationship between the sides of these similar triangles?
3. If another angle was known, could we determine all angles in both triangles?
4. What would happen if the similarity of the triangles was not given?
5. How can similar triangles help in real-world applications like map scaling?

### Tip
When dealing with similar triangles, remember that corresponding angles are always equal, and side lengths have a constant ratio.

Assume that the figures shown to the right are similar. Given the lengths of sides and measures of angles in the left figure, what information is known about the right figure? The measure of angle GEF is __ degrees.

Learn how to find the measure of an angle in a similar triangle given one angle measure and side lengths in another triangle. This problem covers triangle similarity and angle correspondence, ideal for students in Grades 8-10.

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