Question

in which figure do $\angle 1$ and $\angle 2$ represent a pair of alternate exterior angles?

Explanation:

Step1: Recall Alternate Exterior Angles Definition

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 Each Figure

• Top - Left Figure: Check the positions of \( \angle 1 \) and \( \angle 2 \). \( \angle 1 \) is on the left - outer side and \( \angle 2 \) is on the right - outer side of the two parallel lines (vertical lines) cut by the transversal (horizontal line). They are outside the two vertical lines and on alternate sides of the transversal.
• Top - Right Figure: \( \angle 1 \) and \( \angle 2 \) are on the same side of the transversal and \( \angle 2 \) is between the two vertical lines, so they are not alternate exterior angles.
• Bottom - Left Figure: \( \angle 2 \) is between the two vertical lines, so it's not an exterior angle.
• Bottom - Right Figure: \( \angle 1 \) and \( \angle 2 \) are on the same side of the transversal and \( \angle 1 \) is between the two vertical lines (or in a position that doesn't fit alternate exterior angles).

Answer:

The Top - Left Figure (the first figure in the top - left corner of the four - figure grid)