Question

in which figure is $\angle 1$ congruent to $\angle 2$? four figures with lines and angles 1,2

Explanation:

Step1: Recall congruent angle rules

Congruent angles have equal measure. For lines cut by a transversal, corresponding angles (when lines are parallel) are congruent, as are alternate interior/exterior angles, vertical angles.

Step2: Analyze top-left figure

Two non-parallel lines cut by transversal: ∠1 and ∠2 are not corresponding/alternate/vertical, so not congruent.

Step3: Analyze top-right figure

Two parallel horizontal lines cut by transversal: ∠1 and ∠2 are corresponding angles. By corresponding angles postulate, they are congruent.

Step4: Analyze bottom-left figure

Two non-parallel lines cut by transversal: ∠1 and ∠2 are not congruent.

Step5: Analyze bottom-right figure

Two non-parallel lines cut by transversal: ∠1 and ∠2 are not congruent.

Answer:

The top-right figure (with two horizontal parallel lines cut by a slanted transversal, where ∠1 and ∠2 are corresponding angles) has ∠1 congruent to ∠2.