In triangle ABC, the measure of angle A is 48°. Which of the following could be the measure, in degrees,...

1. TRANSLATE the problem information

• Given information:
  • Triangle ABC has angle \(\mathrm{A = 48°}\)
  • Need to find which value could be angle B from the choices

2. INFER the fundamental relationship

• In any triangle, all angles sum to 180°
• This gives us: \(\mathrm{A + B + C = 180°}\)
• Substituting: \(\mathrm{48° + B + C = 180°}\)
• Therefore: \(\mathrm{B + C = 132°}\)

3. INFER the angle constraints

• For a valid triangle, all angles must be positive
• We need \(\mathrm{B \gt 0°}\) and \(\mathrm{C \gt 0°}\)
• Since \(\mathrm{C = 132° - B}\), we need \(\mathrm{132° - B \gt 0°}\)
• This means \(\mathrm{B \lt 132°}\)
• Combined constraint: \(\mathrm{0° \lt B \lt 132°}\)

4. APPLY CONSTRAINTS to check each choice

• Choice A: \(\mathrm{B = 131°}\), so \(\mathrm{C = 132° - 131° = 1°}\) ✓
• Choice B: \(\mathrm{B = 135°}\), so \(\mathrm{C = 132° - 135° = -3°}\) ✗
• Choice C: \(\mathrm{B = 140°}\), so \(\mathrm{C = 132° - 140° = -8°}\) ✗
• Choice D: \(\mathrm{B = 148°}\), so \(\mathrm{C = 132° - 148° = -16°}\) ✗

Answer: A

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak APPLY CONSTRAINTS reasoning: Students correctly find that \(\mathrm{B + C = 132°}\) but fail to check whether the third angle C would be positive for each choice.

They might think: "As long as B is positive, any of these choices work" and either guess randomly or pick the largest value thinking "bigger angles are more likely." This leads to confusion and guessing among the incorrect choices.

Second Most Common Error:

Incomplete INFER process: Students know angles sum to 180° but don't take the next logical step to establish bounds on angle B.

They might calculate \(\mathrm{B + C = 132°}\) but then get stuck, not realizing they can determine which values of B are actually possible. This causes them to get stuck and randomly select an answer.

The Bottom Line:

This problem tests whether students understand that triangle angle constraints go beyond just "angles sum to 180°" - they must also ensure ALL angles remain positive, which creates meaningful restrictions on possible angle measures.