Question

which angles are corresponding angles? ∠3 and ∠7 ∠4 and ∠6 ∠1 and ∠8 ∠1 and ∠7 parallel lines s and t are cut by a transversal r.

Explanation:

Step1: Recall the definition of corresponding angles

Corresponding angles are pairs of angles that are in the same relative position with respect to the parallel lines and the transversal.

Step2: Analyze each option

• For \(\angle3\) and \(\angle7\): They are not in the same relative position. \(\angle3\) is between the parallel lines \(s\) and \(t\) and on one side of transversal \(r\), \(\angle7\) is also between the parallel lines but in a different relative position.
• For \(\angle4\) and \(\angle6\): These are alternate - interior angles, not corresponding angles.
• For \(\angle1\) and \(\angle8\): \(\angle1\) is above line \(s\) and \(\angle8\) is below line \(t\), not in the same relative position.
• For \(\angle1\) and \(\angle7\): \(\angle1\) is in the upper - right position relative to line \(s\) and transversal \(r\), \(\angle7\) is in the upper - right position relative to line \(t\) and transversal \(r\).

Answer:

\(\angle1\) and \(\angle7\)