Question

which of the following angle pairs best describes angles 1 and 8 in the graphic below? graphic of two parallel lines (a and b) cut by a transversal (t), with angles labeled 1,2,3,4,5,6,7,8 options: they are alternate exterior angles. they are vertical angles. they are same - side interior angles. they are alternate interior angles. they are corresponding angles.

Explanation:

Step1: Recall Angle Pair Definitions

• Alternate exterior angles: Lie outside two lines, on opposite sides of a transversal.
• Vertical angles: Opposite angles formed by intersecting lines, equal.
• Same - side interior angles: Inside two lines, same side of transversal.
• Alternate interior angles: Inside two lines, opposite sides of transversal.
• Corresponding angles: Occupy same relative position at each intersection.

Step2: Analyze Angles 1 and 8

• Line \( \alpha \) and \( b \) are the two lines, transversal is \( t \).
• Angle 1 is above line \( \alpha \), left of transversal \( t \). Angle 8 is below line \( b \), right of transversal \( t \). They lie outside the two lines (\( \alpha \) and \( b \)) and on opposite sides of transversal \( t \), matching alternate exterior angles definition.
• Vertical angles: Angle 1 and 3? No, 1 and 3 are adjacent supplementary? Wait, no, vertical angles are like 1 and 4? No, 1 and 3 are adjacent? Wait, no, when two lines intersect, vertical angles are opposite. So angle 1 and 3? No, angle 1 and 4? Wait, no, line \( \alpha \) and \( t \) intersect, angle 1 and 3 are adjacent, angle 1 and 4? No, angle 1 and 3 are supplementary? Wait, no, vertical angles: angle 1 and 3? No, angle 1 and 4? Wait, no, when two lines intersect, vertical angles are equal and opposite. So angle 1 and 3: no, angle 1 and 4? Wait, no, line \( \alpha \) and \( t \) intersect, angle 1 and 3 are adjacent, angle 1 and 4: no, angle 1 and 3 are supplementary? Wait, maybe I messed up. But angle 1 and 8: angle 1 is outside (above \( \alpha \)) and angle 8 is outside (below \( b \)), on opposite sides of \( t \). So alternate exterior.

Answer:

They are alternate exterior angles.