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: Recall the properties of parallel lines and transversals

When two parallel lines (here \(a\) and \(b\)) are cut by a transversal (\(c\)), corresponding angles are equal, alternate - interior angles are equal, and vertical angles are equal. Also, \(\angle2\) and \(\angle4\) are alternate - exterior angles.

Step2: Apply the alternate - exterior angles theorem

The alternate - exterior angles theorem states that if two parallel lines are cut by a transversal, then alternate - exterior angles are congruent. Since \(a\parallel b\) and \(c\) is the transversal, \(\angle2\) and \(\angle4\) are alternate - exterior angles.

Answer:

C. \(\angle4\)