Triangles PQR and STU are congruent, where P corresponds to S, Q corresponds to T, and R corresponds to U....

1. TRANSLATE the problem information

• Given information:
  • Triangles PQR and STU are congruent
  • \(\mathrm{P ↔ S, Q ↔ T, R ↔ U}\) (correspondence)
  • \(\mathrm{Angle\ P = 35°}\)
  • \(\mathrm{Angle\ Q = 90°}\) (right angle)
  • \(\mathrm{Exterior\ angle\ at\ U = 125°}\)

• What this tells us: We have a congruence relationship with specific angle correspondences.

2. INFER the key relationship

• Since the triangles are congruent, corresponding angles must be equal
• The most direct path: Q corresponds to T, so \(\mathrm{angle\ T = angle\ Q}\)
• Since \(\mathrm{angle\ Q = 90°}\), then \(\mathrm{angle\ T = 90°}\)

3. Verify our answer makes sense

The exterior angle at U = 125° means interior angle U = 180° - 125° = 55°
Since R corresponds to U, angle R = 55°
Triangle PQR check: \(\mathrm{35° + 90° + 55° = 180°}\) ✓

Answer: C (90°)

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak INFER skill: Students get overwhelmed by the exterior angle information and don't recognize the direct correspondence relationship.

Instead of using \(\mathrm{Q ↔ T}\) directly, they might try to work backwards from the exterior angle at U, calculating interior angle U = 55°, then assuming angle T also equals 55° (confusing the correspondences). This may lead them to select Choice B (55°).

Second Most Common Error:

Conceptual confusion about correspondences: Students might confuse which angles correspond to which, potentially thinking T corresponds to a different vertex.

If they incorrectly think T corresponds to R (instead of Q), they might conclude angle T = 55°, again leading to Choice B (55°).

The Bottom Line:

The key insight is recognizing that congruent triangles give you direct equality of corresponding angles - no complex calculations needed when you have a direct correspondence like \(\mathrm{Q ↔ T}\).