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 \(\text{angle B} = 63°\) and \(\text{angle C} = 42°\)
  • 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: \(\text{Exterior angle at A} = \text{angle B} + \text{angle C}\)
• Calculate: \(63° + 42° = 105°\)

Answer: D (\(105°\))

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

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.