Geometry

Question Analysis

This question involves finding the missing angle. The main focus is on understanding the properties of parallel lines cut by a transversal.

Key Concept Explanation:

When two parallel lines are cut by a transversal, same-side interior angles are on the same side of the transversal and inside the two lines. The key property is that same-side interior angles are supplementary.

Step-by-Step Solution:

∵ m∥n (Given)

∴ m∠4 + m∠7 = 180° (Same-Side Interior Angles Theorem)

∵ m∠7 = 37° (Given)

∴ m∠7 + 37°= 180° (Substitution)

∴ m∠7 = 180° - 37° ...