Question

analyze the diagram below and answer the question that follows.
in the figure, which angle has the same measure as \\( \angle 2 \\)?
a. \\( \angle 1 \\)
b. \\( \angle 3 \\)
c. \\( \angle 4 \\)
d. \\( \angle 5 \\)

Explanation:

Step1: Identify parallel lines and transversal

Lines \(a\) and \(b\) are parallel (marked with red arrows), and line \(c\) is a transversal.

Step2: Use the property of alternate - interior angles

\(\angle2\) and \(\angle4\) are alternate - interior angles.
By the Alternate - Interior Angles Theorem, if two parallel lines are cut by a transversal, then alternate - interior angles are congruent.

Answer:

C. \(\angle4\)