in which figure is ∠1 congruent to ∠2?

Answer

Explanation:

Step1: Recall congruent - angle rules

Vertical angles are congruent. Corresponding angles formed by parallel lines and a transversal are congruent.

Step2: Analyze first figure

In the first figure, (\angle1) and (\angle2) are corresponding angles formed by two parallel lines and a transversal. By the corresponding - angles postulate, if two parallel lines are cut by a transversal, corresponding angles are congruent. So (\angle1\cong\angle2) in the first figure.

Step3: Analyze second figure

In the second figure, (\angle1) and (\angle2) are not vertical angles, and there is no indication of parallel lines to suggest they are corresponding or alternate - interior/exterior angles. So they are not congruent.

Step4: Analyze third figure

In the third figure, (\angle1) and (\angle2) are not vertical angles, and there is no indication of parallel lines to suggest they are corresponding or alternate - interior/exterior angles. So they are not congruent.

Step5: Analyze fourth figure

In the fourth figure, (\angle1) and (\angle2) are not vertical angles, and there is no indication of parallel lines to suggest they are corresponding or alternate - interior/exterior angles. So they are not congruent.

Answer:

The first figure.