Question

analyze the diagram below and complete the instructions that follow.
find the measure of \\( \angle 2 \\). state the postulate or theorem used to justify your answer.
a. \\( 72 ^ { \circ } \\), alternate interior angles theorem
b. \\( 72 ^ { \circ } \\), alternate exterior angles theorem
c. \\( 108 ^ { \circ } \\), corresponding angles postulate
d. \\( 108 ^ { \circ } \\), consecutive exterior angles theorem

Explanation:

Step1: Recall the alternate interior angles theorem

The alternate interior angles theorem states that if two parallel lines are cut by a transversal, then alternate interior angles are congruent.

Step2: Identify the relationship between the given angle and ∠2

Here, the \(72^{\circ}\) angle and ∠2 are alternate interior angles. Since the lines \(a\) and \(b\) (with the arrowheads) are parallel (as indicated by the arrow - like markings) and cut by the transversal \(c\).

Answer:

A. \(72^{\circ}\), alternate interior angles theorem