In triangle ABC, the measure of angle B is 63° and the measure of angle C is 42°. What is...

1. TRANSLATE the problem information

• Given information:
  • Triangle ABC with \(\mathrm{angle\ B = 63°}\) and \(\mathrm{angle\ C = 42°}\)
  • Need to find the exterior angle at vertex A

• What this tells us: We're looking for an angle outside the triangle at vertex A, and we have the measures of the two angles that are not at vertex A.

2. INFER the approach

• Key insight: This is a perfect setup for the Exterior Angle Theorem
• The exterior angle at vertex A will equal the sum of the two remote interior angles (angles B and C)
• We don't need to find interior angle A first

3. SIMPLIFY using the Exterior Angle Theorem

• Apply the theorem: Exterior angle at A = angle B + angle C
• Calculate: \(\mathrm{63° + 42° = 105°}\)

Answer: D (\(\mathrm{105°}\))

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak INFER skill: Students don't recognize the Exterior Angle Theorem and instead try to find the interior angle at A first.

They calculate: \(\mathrm{angle\ A = 180° - 63° - 42° = 75°}\), then mistakenly think this interior angle is their final answer. This may lead them to select Choice C (\(\mathrm{75°}\)).

Second Most Common Error:

Poor TRANSLATE reasoning: Students confuse which angles are "remote" for the exterior angle at vertex A.

They might incorrectly think they need to add angle A to one of the other angles, or get confused about what "exterior angle at vertex A" actually means. This leads to confusion and guessing among the remaining choices.

The Bottom Line:

This problem tests whether students can directly apply the Exterior Angle Theorem instead of taking the longer route through interior angle calculations. The key insight is recognizing that angles B and C are exactly what you need - no additional steps required.