Question

which angles are corresponding angles with angle 8?
∠4 and ∠12
∠2 and ∠10
∠6 and ∠14
∠3 and ∠9

Explanation:

Step1: Recall the definition of corresponding angles

Corresponding angles are in the same relative position at each intersection where a straight - line crosses two others.

Step2: Analyze each option

• For \(\angle4\) and \(\angle12\): \(\angle4\) and \(\angle8\) are not in the same relative position. \(\angle12\) and \(\angle8\) are not in the same relative position.
• For \(\angle2\) and \(\angle10\): \(\angle2\) and \(\angle8\) are not in the same relative position. \(\angle10\) and \(\angle8\) are not in the same relative position.
• For \(\angle6\) and \(\angle14\): \(\angle6\) and \(\angle8\) are adjacent. \(\angle14\) and \(\angle8\) are not in the same relative position.
• For \(\angle3\) and \(\angle9\):
• \(\angle3\) and \(\angle8\): When considering the intersection of line \(r\) with lines \(t\) and \(s\), \(\angle3\) and \(\angle8\) are not corresponding. But when considering the parallel lines \(t\) and \(u\) cut by transversal \(s\), \(\angle3\) (at the intersection of \(r\) and \(t\)) and \(\angle9\) (at the intersection of \(r\) and \(u\)) are in the same relative position as \(\angle8\) (at the intersection of \(s\) and \(t\)) and \(\angle9\) (at the intersection of \(s\) and \(u\)) with respect to the parallel lines \(t\) and \(u\) and transversals \(r\) and \(s\).

Answer:

\(\angle3\) and \(\angle9\)