Triangle ABC is transformed by a rotation followed by a dilation to create triangle A'B'C'. Under this transformation, vertex A...

1. TRANSLATE the transformation information

• Given information:
  • Triangle ABC transformed by rotation + dilation → triangle A′B′C′
  • Vertex mapping: A → B′ and C → A′
  • \(\mathrm{m∠C = 37°}\) in original triangle
  • Find: \(\mathrm{m∠A'}\) in transformed triangle

2. INFER the key property of the transformation

• Rotation followed by dilation = similarity transformation
• Similarity transformations preserve all angle measures
• This means triangle A′B′C′ is similar to triangle ABC

3. INFER which angles correspond

• From the mapping C → A′, vertex C corresponds to vertex A′
• Therefore, angle C in triangle ABC corresponds to angle A′ in triangle A′B′C′

4. Apply the similarity property

• Since corresponding angles in similar triangles are equal:
• \(\mathrm{m∠A' = m∠C = 37°}\)

Answer: A (37°)

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Not properly interpreting the mapping notation "C maps to A′"

Students might misread this as meaning angle A corresponds to angle A′ instead of angle C corresponding to angle A′. They see "A′" in the question and think it must relate to vertex A, missing that the mapping explicitly states C → A′.

This may lead them to look for the measure of angle A instead, or to guess randomly among the choices.

Second Most Common Error:

Missing conceptual knowledge about similarity transformations: Not recognizing that rotation + dilation preserves angle measures

Students might think the angles change during transformation, especially if they focus on the dilation part and think "scaling changes everything." They might try to calculate some proportional relationship or apply the 37° in some complex way.

This leads to confusion and guessing among the other answer choices.

The Bottom Line:

This problem tests whether students understand that similarity transformations preserve angles and whether they can correctly interpret vertex mapping notation. The key insight is that despite the complex-sounding transformation, the angles remain unchanged in similar figures.