Question:Angle A measures 5pi/6 radians. Angle B measures 135°. What is the measure of angle A minus angle B, in...

1. TRANSLATE the problem information

• Given information:
  • Angle A = \(\frac{5\pi}{6}\) radians
  • Angle B = \(135°\)
  • Find: Angle A - Angle B (in degrees)

• What this tells us: We have two angles in different units that need to be subtracted, so unit conversion is required first.

2. TRANSLATE the solution approach

• Key insight: Cannot subtract angles in different units
• Strategy: Convert angle A from radians to degrees, then subtract angle B
• Use the conversion formula: \(\mathrm{degrees} = \mathrm{radians} \times \frac{180}{\pi}\)

3. SIMPLIFY the radian to degree conversion

• Apply the conversion formula:
  Angle A = \(\frac{5\pi}{6} \times \frac{180}{\pi}\)

• Cancel out π terms:
  \(= \frac{5 \times 180}{6}\)

• Complete the arithmetic:
  \(= \frac{900}{6} = 150°\)

4. Subtract the angles

• Now both angles are in degrees:
  Angle A - Angle B = \(150° - 135° = 15°\)

Answer: (A) 15°

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Not recognizing that the angles are in different units and attempting to subtract them directly.

Students might try to compute \(\frac{5\pi}{6} - 135°\) without realizing this operation is meaningless. They get confused by mixing radians and degrees, leading them to abandon systematic solution and guess randomly among the choices.

Second Most Common Error:

Conceptual confusion about unit conversion: Using the wrong conversion formula, such as \(\mathrm{degrees} = \mathrm{radians} \times \frac{\pi}{180}\) instead of the correct formula \(\mathrm{degrees} = \mathrm{radians} \times \frac{180}{\pi}\).

This would give Angle A = \(\frac{5\pi}{6} \times \frac{\pi}{180} = \frac{5\pi^2}{1080}\), which doesn't simplify to a clean degree measure. Students recognize something is wrong but may incorrectly calculate and potentially select Choice (D) (150°) thinking that's the converted angle value.

The Bottom Line:

This problem tests whether students can recognize when unit conversion is necessary and remember the correct conversion formula. The mathematical operations are straightforward once the units are aligned.