Question

which angles are congruent to each other?
∠6 and ∠7 ∠9 and ∠12 ∠4 and ∠2 ∠12 and ∠1

Explanation:

Step1: Recall the definition of vertical angles

Vertical angles are opposite angles formed by two intersecting lines and are congruent.

Step2: Analyze each option

• For $\angle6$ and $\angle7$: They are adjacent angles (form a linear - pair), not vertical angles. So they are not congruent.
• For $\angle9$ and $\angle12$: They are vertical angles (formed by the intersection of two lines). By the vertical - angles theorem, vertical angles are congruent.
• For $\angle4$ and $\angle2$: They are adjacent angles (form a linear - pair), not vertical angles. So they are not congruent.
• For $\angle12$ and $\angle1$: They are not vertical angles.

Answer:

$\angle9$ and $\angle12$