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 \\( \angle \\) symbol in your answer.)

Explanation:

Step1: Identify vertical angles

Vertical angles are congruent. Angle \(2\) and the given angle are vertical angles. So \(2\) is congruent to the given angle.

Step2: Use corresponding angles

Since the two horizontal lines are parallel, corresponding angles are congruent. The given angle and angle \(6\) are corresponding angles. So \(6\) is congruent to the given angle.

Step3: Use alternate - interior angles

Angle \(2\) and angle \(8\) are alternate - interior angles (because of the parallel lines). Since angle \(2\) is congruent to the given angle (from step 1) and \(2\cong8\) (alternate - interior angles), then \(8\) is congruent to the given angle.

Answer:

\(2,6,8\)