Question

use the image to answer the question
given that ( mangle3 ) is ( 75^{circ} ), which theorem could be used to find ( mangle5 )?
(1 point)
consecutive exterior angles theorem
alternate interior angles theorem
alternate exterior angles theorem
consecutive interior angles theorem

Explanation:

• Alternate interior angles are formed when a transversal crosses two parallel lines.
• In the given figure, lines \(m\) and \(n\) are parallel and \(k\) is a transversal.
• \(\angle3\) and \(\angle5\) 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:

Alternate Interior Angles Theorem