Given two parallel lines cut by a transversal, if one of the alternate interior angles measures $k$ degrees and the other measures $71$ degrees, what is the value of $k$?

• A. $k=60$
• B. $k=71$
• C. $k=9$
• D. $k=20$

Answer: (B)

Verified step by step guidance

1. Recall that when two parallel lines are cut by a transversal, alternate interior angles are congruent, meaning they have equal measures.
2. Identify the given alternate interior angles: one angle measures \(k\) degrees and the other measures 71 degrees.
3. Set up the equation based on the property of alternate interior angles: \(k = 71\).
4. Solve the equation for \(k\) by recognizing that since the angles are equal, \(k\) must be 71 degrees.
5. Conclude that the value of \(k\) is 71 degrees because alternate interior angles formed by parallel lines and a transversal are equal.