Right triangles LMN and PQR are similar, where L and M correspond to P and Q, respectively. Angle M has...
GMAT Geometry & Trigonometry : (Geo_Trig) Questions
Right triangles \(\mathrm{LMN}\) and \(\mathrm{PQR}\) are similar, where \(\mathrm{L}\) and \(\mathrm{M}\) correspond to \(\mathrm{P}\) and \(\mathrm{Q}\), respectively. Angle \(\mathrm{M}\) has a measure of \(53°\). What is the measure of angle \(\mathrm{Q}\)?
37°
53°
127°
143°
1. TRANSLATE the problem information
- Given information:
- Right triangles LMN and PQR are similar
- L corresponds to P, M corresponds to Q
- Angle M = \(53°\)
- Need to find: measure of angle Q
- What this tells us: We have a correspondence between the vertices of two similar triangles, and we know one angle measure.
2. INFER the key relationship
- Since the triangles are similar, corresponding angles must be congruent
- M corresponds to Q means angle M and angle Q are corresponding angles
- Therefore: angle M = angle Q
3. Apply the relationship
- If angle M = \(53°\), then angle Q = \(53°\)
Answer: B. \(53°\)
Why Students Usually Falter on This Problem
Most Common Error Path:
Weak TRANSLATE skill: Students misinterpret the correspondence statement and think they need to find a different angle relationship.
Some students might think "corresponding" means the angles are supplementary (add to \(180°\)) or complementary (add to \(90°\)), leading them to calculate:
\(180° - 53° = 127°\)
or
\(90° - 53° = 37°\)
This may lead them to select Choice A (\(37°\)) or Choice C (\(127°\)).
The Bottom Line:
The key insight is recognizing that "corresponding angles in similar triangles are congruent" is a direct, one-step relationship. No calculations with angle measures are needed—just identify which angles correspond and apply the congruence property.
37°
53°
127°
143°