Question

in which figure is ∠1 congruent to ∠2? (four figures with lines and angles ∠1, ∠2 are shown)

Explanation:

Step1: Recall congruent angle rules

Congruent angles have equal measure. Key rules: vertical angles are congruent; corresponding angles formed by a transversal on parallel lines are congruent.

Step2: Analyze top-left figure

∠1 and ∠2 are vertical angles. By vertical angle theorem, vertical angles are congruent.

Step3: Verify other figures

Top-right: ∠1, ∠2 are not vertical/corresponding, no parallel lines. Bottom-left: No parallel lines, angles not congruent. Bottom-right: ∠1, ∠2 are not corresponding congruent angles.

Answer:

The top-left figure (where ∠1 and ∠2 are vertical angles) is the one where ∠1 is congruent to ∠2.