In the figure, two parallel lines are cut by a transversal. angle 3 and angle 4 are corresponding angles. The...

1. TRANSLATE the problem information

• Given information:
  • Two parallel lines cut by a transversal
  • Angle 3 = 58°
  • Angles 3 and 4 are corresponding angles

• What this tells us: We need to find the measure of angle 4, which has a specific geometric relationship with angle 3.

2. INFER what geometric theorem applies

• When you see parallel lines cut by a transversal, several angle relationships exist:
  • Corresponding angles (same position at each intersection)
  • Alternate interior angles (inside the parallel lines, on opposite sides)
  • Supplementary angles (linear pairs that add to 180°)

• The problem explicitly states that angles 3 and 4 are corresponding angles.

• Key insight: The corresponding angles theorem tells us that when parallel lines are cut by a transversal, corresponding angles are congruent (equal in measure).

3. Apply the corresponding angles theorem

• Since angles 3 and 4 are corresponding angles formed by parallel lines and a transversal:

\(\mathrm{Angle\,4 = Angle\,3}\)

• Therefore:

\(\mathrm{Angle\,4 = 58°}\)

Answer: 58° (Choice B)

Why Students Usually Falter on This Problem

Most Common Error Path:

Conceptual confusion about angle relationships: Students may confuse corresponding angles with other angle pairs formed by a transversal.

If a student thinks angles 3 and 4 are supplementary (forming a linear pair), they would calculate:

• \(\mathrm{Angle\,4 = 180° - 58° = 122°}\)

This may lead them to select Choice C (122°).

Second Most Common Error:

Weak INFER skill - applying complementary angle relationship: Students might mistakenly think the angles are complementary (adding to 90°), perhaps confusing angle relationships or not recognizing the parallel lines context.

They would calculate:

• \(\mathrm{Angle\,4 = 90° - 58° = 32°}\)

This may lead them to select Choice A (32°).

The Bottom Line:

This problem tests whether students can identify corresponding angles in a diagram and recall that corresponding angles are congruent when formed by parallel lines and a transversal. The key is not getting confused by other angle relationships and directly applying the correct theorem. The presence of answer choices like 32° and 122° specifically targets common misconceptions about angle relationships.