Question

parallel lines r and s are cut by two transversals, parallel lines t and u. how many angles are alternate interior angles with angle 9?

Explanation:

Step1: Recall the definition of alternate interior angles

Alternate interior angles are formed when two parallel lines are cut by a transversal. They lie between the two parallel lines and on opposite sides of the transversal.

Step2: Identify the transversals and parallel lines

Here, parallel lines \(r\) and \(s\) are cut by transversals \(t\) and \(u\). For angle \(9\), consider the pairs of parallel lines and transversals.

• When considering transversal \(u\) and parallel lines \(s\) and \(r\): There is no alternate - interior relationship relevant here for angle \(9\) in the context of the given figure.
• When considering transversal \(s\) and parallel lines \(t\) and \(u\): Angle \(3\) is an alternate - interior angle with angle \(9\) (since \(t\parallel u\) and \(s\) is the transversal).
• When considering transversal \(r\) and parallel lines \(t\) and \(u\): There is no valid alternate - interior pair for angle \(9\) in the given figure.
• When considering transversal \(t\) and parallel lines \(r\) and \(s\): There is no valid alternate - interior pair for angle \(9\) in the given figure.

Answer:

\(1\)