In triangle JKL, the measures of angleK and angleL are each 48°. What is the measure of angleJ, in degrees?...

1. TRANSLATE the problem information

• Given information:
  • Triangle JKL with \(\angle\mathrm{K} = 48°\) and \(\angle\mathrm{L} = 48°\)
  • Need to find the measure of \(\angle\mathrm{J}\)

2. INFER the approach

• Since we have a triangle with two known angles, we can use the fundamental property that all interior angles in a triangle sum to 180°
• This means: \(\angle\mathrm{J} + \angle\mathrm{K} + \angle\mathrm{L} = 180°\)

3. TRANSLATE into equation form

• Substitute the known values: \(\angle\mathrm{J} + 48° + 48° = 180°\)
• Combine like terms: \(\angle\mathrm{J} + 96° = 180°\)

4. SIMPLIFY to find the answer

• Solve for \(\angle\mathrm{J}\): \(\angle\mathrm{J} = 180° - 96° = 84°\)

Answer: 84

Why Students Usually Falter on This Problem

Most Common Error Path:

Missing conceptual knowledge: Not remembering that triangle interior angles sum to 180°

Students may recognize this is a triangle problem but get stuck because they don't recall this fundamental property. Without this key concept, they have no systematic way to find the missing angle and resort to guessing.

Second Most Common Error:

Weak SIMPLIFY execution: Making arithmetic errors in the calculation

Some students correctly set up \(\angle\mathrm{J} = 180° - 48° - 48°\) but then calculate incorrectly, perhaps getting \(180° - 48° = 132°\) first, then \(132° - 48° = 94°\) instead of the correct 84°.

The Bottom Line:

This problem tests whether students can recall and apply one of the most fundamental properties in geometry. The setup is straightforward once you know the triangle angle sum property, making conceptual knowledge the primary challenge rather than complex reasoning.