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 property

Vertical angles are congruent. $\angle1$ and $\angle3$, $\angle2$ and $\angle4$, $\angle5$ and $\angle7$, $\angle6$ and $\angle8$ are vertical angles.

Step2: Recall corresponding - angle property

If two parallel lines are cut by a transversal, corresponding angles are congruent. Here, assuming the two horizontal lines are parallel, $\angle1$ and $\angle5$, $\angle2$ and $\angle6$, $\angle3$ and $\angle7$, $\angle4$ and $\angle8$ are corresponding angles.

Step3: Recall alternate - interior and alternate - exterior angle properties

Alternate - interior angles are congruent. $\angle2$ and $\angle5$, $\angle3$ and $\angle8$ are alternate - interior angles. Alternate - exterior angles are congruent. $\angle1$ and $\angle8$, $\angle4$ and $\angle7$ are alternate - exterior angles.

Answer:

D. $\angle1$ and $\angle8$