Question

what is the relationship between \\(\angle 1\\) and \\(\angle 2\\)? match each figure with the angle relationship it shows.

(1) alternate exterior angles

Explanation:

Step1: Recall Alternate Exterior Angles

Alternate exterior angles are formed when a transversal crosses two parallel lines. They lie outside the two lines and on opposite sides of the transversal.

Step2: Analyze the Figures

• The top - right figure: ∠1 and ∠2 are inside the two parallel lines and on the same side of the transversal? No, wait, let's re - check. Wait, the bottom - left figure: Let's see the positions. Wait, the angle relationship "alternate exterior angles" should match the figure where ∠1 and ∠2 are outside the two parallel lines and on opposite sides of the transversal. Wait, maybe I made a mistake. Wait, the standard definition: Alternate exterior angles are two angles that lie outside the two lines cut by a transversal and are on opposite sides of the transversal. Let's look at the bottom - left figure: ∠1 is above the top line and to the left of the transversal, ∠2 is below the bottom line and to the right of the transversal? No. Wait, the top - right figure: ∠1 is above the top line and to the right of the transversal, ∠2 is below the bottom line and to the left of the transversal? No. Wait, maybe the bottom - left figure: Wait, no, let's think again. The angle relationship "alternate exterior angles" should be matched with the figure where ∠1 and ∠2 are exterior (outside the two parallel lines) and alternate (on opposite sides of the transversal). Let's check the bottom - left figure: The two parallel lines, the transversal. ∠1 is on the top line, outside the two lines (above the top line) and to the left of the transversal. ∠2 is on the bottom line, outside the two lines (below the bottom line) and to the right of the transversal. Wait, no, maybe the bottom - left figure is the one with alternate exterior angles? Wait, no, let's look at the options. The first box is "alternate exterior angles", and we need to match it with the correct figure. The bottom - left figure: Let's see the positions. The top - right figure: ∠1 and ∠2 are alternate interior angles? No. Wait, the bottom - left figure: ∠1 is above the top parallel line, ∠2 is below the bottom parallel line, and they are on opposite sides of the transversal. So that's alternate exterior angles. Wait, maybe I messed up the figures. Wait, the problem is to match "alternate exterior angles" with the correct figure. The bottom - left figure (the one in the second row, first column) has ∠1 and ∠2 as alternate exterior angles. Wait, no, let's check the standard diagram. Alternate exterior angles: when two parallel lines are cut by a transversal, alternate exterior angles are equal. The figure where ∠1 is outside the two lines (above the top line) and ∠2 is outside the two lines (below the bottom line), and on opposite sides of the transversal. So the bottom - left figure (second row, first column) is the one that shows alternate exterior angles. Wait, but the first box is "alternate exterior angles", so we need to match it with the correct figure. So the "alternate exterior angles" should be matched with the bottom - left figure (the figure in the second row, first column).

Answer:

The "alternate exterior angles" should be matched with the bottom - left figure (the figure in the second row, first column).