Question:In triangle ABC, angle A is 3 degrees more than twice angle B.angle C measures 42^circ.What is the measure of...

1. TRANSLATE the problem information

• Given information:
  • Angle A is 3 degrees more than twice angle B → \(\mathrm{A = 2B + 3}\)
  • Angle C = 42 degrees
  • We need to find the measure of angle A

2. INFER the approach

• Since we have a triangle, we know \(\mathrm{A + B + C = 180}\)
• We have one angle (\(\mathrm{C = 42}\)) and a relationship between A and B
• Strategy: Use substitution to solve for B first, then find A

3. Set up the main equation

• Triangle angle sum: \(\mathrm{A + B + C = 180}\)
• Substitute \(\mathrm{C = 42}\): \(\mathrm{A + B + 42 = 180}\)
• Therefore: \(\mathrm{A + B = 138}\)

4. SIMPLIFY using substitution

• Substitute \(\mathrm{A = 2B + 3}\) into \(\mathrm{A + B = 138}\):
• \(\mathrm{(2B + 3) + B = 138}\)
• \(\mathrm{3B + 3 = 138}\)
• \(\mathrm{3B = 135}\)
• \(\mathrm{B = 45}\)

5. Find angle A

• \(\mathrm{A = 2B + 3 = 2(45) + 3 = 90 + 3 = 93}\)

6. Verify the solution

• Check: \(\mathrm{A + B + C = 93 + 45 + 42 = 180}\) ✓

Answer: C (93)

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Students struggle to convert "angle A is 3 degrees more than twice angle B" into the correct algebraic expression. They might write \(\mathrm{A = 2B - 3}\) (subtracting instead of adding) or \(\mathrm{A = 3B + 2}\) (mixing up the coefficients).

If they use \(\mathrm{A = 2B - 3}\), they get:

\(\mathrm{(2B - 3) + B = 138}\)
\(\mathrm{3B - 3 = 138}\)
\(\mathrm{3B = 141}\)
\(\mathrm{B = 47}\)

then \(\mathrm{A = 2(47) - 3 = 91}\). This doesn't match any answer choice, leading to confusion and guessing.

Second Most Common Error:

Poor SIMPLIFY execution: Students make arithmetic errors in the algebra, particularly when combining like terms or solving \(\mathrm{3B = 135}\). They might calculate \(\mathrm{B = 44}\) or \(\mathrm{B = 46}\) instead of \(\mathrm{B = 45}\).

With \(\mathrm{B = 44}\): \(\mathrm{A = 2(44) + 3 = 91}\) (not an answer choice)
With \(\mathrm{B = 46}\): \(\mathrm{A = 2(46) + 3 = 95}\) (close to choice D: 96, might select this)

This may lead them to select Choice D (96) due to the arithmetic error.

The Bottom Line:

This problem tests your ability to carefully translate word relationships into algebra and execute the solution accurately. The key insight is recognizing that triangle problems often require combining given angle relationships with the fundamental property that angles sum to 180 degrees.