Question

which angles are congruent to each other? ∠5 and ∠7 ∠6 and ∠10 ∠4 and ∠9 ∠2 and ∠10

Explanation:

Step1: Recall vertical - angle property

Vertical angles are congruent. Also, corresponding angles, alternate - interior angles and alternate - exterior angles formed by parallel lines and a transversal are congruent.

Step2: Analyze ∠5 and ∠7

∠5 and ∠7 are vertical angles. By the vertical - angle theorem, vertical angles are congruent.

Step3: Analyze ∠6 and ∠10

∠6 and ∠10 are not corresponding, alternate - interior, alternate - exterior or vertical angles, so they are not necessarily congruent.

Step4: Analyze ∠4 and ∠9

∠4 and ∠9 are not corresponding, alternate - interior, alternate - exterior or vertical angles, so they are not necessarily congruent.

Step5: Analyze ∠2 and ∠10

∠2 and ∠10 are not corresponding, alternate - interior, alternate - exterior or vertical angles, so they are not necessarily congruent.

Answer:

∠5 and ∠7