Question

given that the two horizontal lines are parallel, identify all the numbered angles that are congruent to the given angle. list the numbers of any angles that are congruent to the given angle. (use a comma to separate answers as needed. do not include the ∠ symbol in your answer.)

Explanation:

Step1: Vertical angles

Vertical angles are congruent. $\angle3$ and the $57^{\circ}$ angle are vertical angles, so $\angle3 = 57^{\circ}$.

Step2: Corresponding angles

Corresponding angles are congruent when two parallel lines are cut by a transversal. $\angle7$ and the $57^{\circ}$ angle are corresponding angles, so $\angle7 = 57^{\circ}$.

Step3: Alternate - interior angles

Alternate - interior angles are congruent when two parallel lines are cut by a transversal. $\angle6$ and the $57^{\circ}$ angle are alternate - interior angles, so $\angle6 = 57^{\circ}$.

Step4: Vertical angles again

Since $\angle6$ and $\angle4$ are vertical angles, $\angle4=\angle6 = 57^{\circ}$.

Answer:

3,4,6,7