Question

which pairs of angles are congruent because they are vertical angles? choose two correct answers. ∠10 and ∠8 ∠8 and ∠12 ∠1 and ∠4 ∠7 and ∠8 ∠3 and ∠8

Explanation:

Step1: Recall vertical angles definition

Vertical angles are formed when two lines intersect. They are opposite each other and are congruent.

Step2: Analyze each pair

• For $\angle10$ and $\angle8$: They are formed by the intersection of two lines. By the vertical - angles theorem, they are congruent.
• For $\angle7$ and $\angle8$: They are adjacent and form a linear pair (sum to \(180^{\circ}\) if they are on a straight - line - like intersection), not vertical angles.
• For $\angle8$ and $\angle12$: They are not formed by the intersection of the same two lines.
• For $\angle1$ and $\angle4$: They are not formed by the intersection of the same two lines.
• For $\angle3$ and $\angle8$: They are not formed by the intersection of the same two lines.

Answer:

\(\angle10\) and \(\angle8\)