Question

which angles are congruent to each other?
∠8 and ∠6 ∠6 and ∠2 ∠6 and ∠5 ∠2 and ∠8

Explanation:

Step1: Recall vertical angles property

Vertical angles are congruent. $\angle6$ and $\angle8$ are vertical angles. $\angle2$ and $\angle4$ are vertical angles. Also, using the property of parallel lines (if we assume the two horizontal - like lines are parallel) and transversal: Corresponding angles are congruent. $\angle6$ and $\angle2$ are corresponding angles.

Step2: Check each option

• For $\angle8$ and $\angle6$: They are vertical angles, so $\angle8=\angle6$.
• For $\angle6$ and $\angle2$: If the lines are parallel (by the corresponding angles postulate), $\angle6=\angle2$.
• For $\angle6$ and $\angle5$: $\angle6+\angle5 = 180^{\circ}$ (they are adjacent and form a linear pair), so they are not congruent.
• For $\angle2$ and $\angle8$: Since $\angle6=\angle8$ (vertical angles) and $\angle6 = \angle2$ (corresponding angles if lines are parallel), then $\angle2=\angle8$.

Answer:

$\angle8$ and $\angle6$, $\angle6$ and $\angle2$, $\angle2$ and $\angle8$