The measure of angle R is 2pi/3 radians. The measure of angle T is 5pi/12 radians greater than the measure...

1. TRANSLATE the problem information

• Given information:
  • Angle R = \(\mathrm{\frac{2\pi}{3}}\) radians
  • Angle T is \(\mathrm{\frac{5\pi}{12}}\) radians greater than angle R
  • Need to find angle T in degrees
• This tells us: \(\mathrm{T = R + \frac{5\pi}{12}}\)

2. SIMPLIFY the angle calculation

• Substitute the value of R:
  \(\mathrm{T = \frac{2\pi}{3} + \frac{5\pi}{12}}\)
• Find common denominator (12):
  \(\mathrm{\frac{2\pi}{3} = \frac{8\pi}{12}}\)
• Add the fractions:
  \(\mathrm{T = \frac{8\pi}{12} + \frac{5\pi}{12} = \frac{13\pi}{12}}\) radians

3. INFER the need for unit conversion

• The problem asks for the answer in degrees, but we have radians
• Use the conversion: multiply by \(\mathrm{\frac{180}{\pi}}\) to convert radians to degrees

4. SIMPLIFY the unit conversion

• \(\mathrm{T = \frac{13\pi}{12} \times \frac{180}{\pi}}\)
• Cancel π: \(\mathrm{T = \frac{13 \times 180}{12}}\)
• Calculate: \(\mathrm{T = \frac{2340}{12} = 195}\) degrees

Answer: C. 195

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak INFER skill: Forgetting to convert units from radians to degrees

Students correctly calculate T = \(\mathrm{\frac{13\pi}{12}}\) radians but give this as their final answer or try to match it to answer choices without converting. Since \(\mathrm{\frac{13\pi}{12} \approx 3.4}\), this doesn't match any answer choice, leading to confusion and guessing.

Second Most Common Error:

Poor SIMPLIFY execution: Errors in fraction addition

Students may struggle with finding the common denominator or make arithmetic mistakes when adding \(\mathrm{\frac{2\pi}{3} + \frac{5\pi}{12}}\). Getting \(\mathrm{\frac{3\pi}{12}}\) instead of \(\mathrm{\frac{13\pi}{12}}\) would lead to T = 45 degrees, which isn't among the choices, causing them to select Choice A (75) as the closest option.

The Bottom Line:

This problem tests both fraction manipulation skills and unit conversion awareness. The key insight is recognizing that angle problems often require careful attention to units in the question versus units in given information.