Question

parallel lines r and s are cut by two transversals, parallel lines t and u. which angles are alternate interior angles with ∠3? ∠8 and ∠14 ∠6 and ∠16 ∠7 and ∠15 ∠5 and ∠13

Explanation:

Step1: Recall the definition of alternate interior angles

Alternate interior angles are non - adjacent interior angles that lie on opposite sides of the transversal.

Step2: Analyze each pair

• For \(\angle8\) and \(\angle14\):
• The transversal is line \(u\), and the parallel lines are \(r\) and \(s\).
• \(\angle8\) and \(\angle14\) are non - adjacent interior angles on opposite sides of transversal \(u\).
• For \(\angle6\) and \(\angle16\):
• \(\angle6\) and \(\angle16\) do not meet the criteria of alternate interior angles as they are not in the correct position relative to the parallel lines and transversal.
• For \(\angle7\) and \(\angle15\):
• \(\angle7\) and \(\angle15\) do not meet the criteria of alternate interior angles as they are not in the correct position relative to the parallel lines and transversal.
• For \(\angle5\) and \(\angle13\):
• \(\angle5\) and \(\angle13\) do not meet the criteria of alternate interior angles as they are not in the correct position relative to the parallel lines and transversal.

Answer:

\(\angle8\) and \(\angle14\)