Question

which angles are congruent to each other? ∠7 and ∠5 ∠5 and ∠2 ∠2 and ∠7 ∠1 and ∠8

Explanation:

Step1: Recall vertical - angle and corresponding - angle properties

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

Step2: Analyze each option

• For ∠7 and ∠5, they are vertical angles. By the vertical - angle theorem, vertical angles are equal in measure, so ∠7≅∠5.
• For ∠5 and ∠2, they are not vertical angles and not corresponding angles in a way that would make them congruent.
• For ∠2 and ∠7, they are neither vertical nor corresponding angles in a way that would make them congruent.
• For ∠1 and ∠8, they are neither vertical nor corresponding angles in a way that would make them congruent.

Answer:

∠7 and ∠5