Question

which angles are congruent to each other?
∠4 and ∠5 ∠6 and ∠2 ∠8 and ∠6 ∠5 and ∠1

Explanation:

Step1: Recall the concept of congruent angles

Congruent angles are angles that have the same measure.

Step2: Analyze each pair

• For $\angle4$ and $\angle5$: They are alternate interior angles. When two parallel lines are cut by a transversal, alternate interior angles are congruent.
• For $\angle6$ and $\angle2$: There is no property (like alternate - interior, corresponding, vertical etc.) that makes them congruent.
• For $\angle8$ and $\angle6$: They are adjacent angles forming a linear pair ($\angle6+\angle8 = 180^{\circ}$ if the lines are straight), so they are not congruent.
• For $\angle5$ and $\angle1$: There is no property (like alternate - interior, corresponding, vertical etc.) that makes them congruent.

Answer:

$\angle4$ and $\angle5$