Question

in which figure is ∠1 congruent to ∠2?

Explanation:

Step1: Recall vertical angles theorem

Vertical angles are congruent. Vertical angles are formed when two lines intersect.

Step2: Analyze each figure

• First figure: \(\angle1\) and \(\angle2\) are vertical angles (formed by the intersection of two lines).
• Second figure: \(\angle1\) and \(\angle2\) are same - side interior angles (not congruent in general).
• Third figure: \(\angle1\) and \(\angle2\) are not vertical angles (no common vertex formed by intersection of two lines).
• Fourth figure: \(\angle1\) and \(\angle2\) are not vertical angles (no common vertex formed by intersection of two lines).

Answer:

The first figure.