Question

in which figure is $\angle 1$ congruent to $\angle 2$?

Explanation:

Step1: Analyze Top-Left Figure

In the top - left figure, the two vertical - like lines are not parallel (one is vertical, the other is slanted), and the transversal creates angles ∠1 and ∠2. There is no special angle - relationship (like vertical angles, corresponding angles for parallel lines) to make ∠1 ≅ ∠2.

Step2: Analyze Top - Right Figure

In the top - right figure, the two lines with the arrow - heads (the non - vertical ones) are parallel (they have the same slope - like appearance), and the line crossing them is a transversal. ∠1 and ∠2 are alternate interior angles. By the Alternate Interior Angles Theorem, if two parallel lines are cut by a transversal, then alternate interior angles are congruent. So ∠1 ≅ ∠2 here.

Step3: Analyze Bottom - Left Figure

In the bottom - left figure, the two vertical - like lines are parallel, but the transversal creates ∠1 and ∠2. ∠1 and ∠2 are not alternate interior, corresponding or vertical angles in a way that guarantees congruence (they are on different sides of the transversal and the parallel lines, and the angle - forming situation doesn't fit a congruent - angle theorem for parallel lines here).

Step4: Analyze Bottom - Right Figure

In the bottom - right figure, the two lines (one slanted, one horizontal) are not parallel, and the transversal (the vertical line) creates ∠1 and ∠2. There is no theorem - based relationship to make ∠1 ≅ ∠2.

Answer:

The top - right figure (the second figure in the top row)