Question

if ( mangle1 = mangle2 ), which of the following statements is true?
a. ( k parallel j )
b. ( n parallel m )
c. ( ell parallel k )
d. ( ell parallel m )

Explanation:

Step1: Recall the Alternate Interior Angles Theorem

The Alternate Interior Angles Theorem states that if two lines are cut by a transversal and the alternate interior angles are congruent, then the two lines are parallel.

Step2: Identify the angles and lines

In the diagram, \( \angle 1 \) and \( \angle 2 \) are alternate interior angles formed by the transversal (the line that intersects both \( m \) and \( n \)) and the lines \( m \) and \( n \). Given that \( m\angle 1=m\angle 2 \), by the Alternate Interior Angles Theorem, the lines \( m \) and \( n \) (the lines that form these alternate interior angles with the transversal) are parallel. So \( n\parallel m \).

Answer:

B. \( n \parallel m \)