Question

in the following diagram, check all angles that are congruent with angle 2
angle 1
angle 3
angle 4
angle 5
angle 6
angle 7
angle 8

Explanation:

Step1: Identify vertical angles

Vertical angles are congruent. Angle 2 and angle 4 are vertical angles, so angle 4 is congruent to angle 2.

Step2: Use parallel - line properties (alternate interior angles)

Since lines \(m\) and \(l\) are parallel, and we consider the transversal. Angle 2 and angle 6 are alternate interior angles. So angle 6 is congruent to angle 2.

Step3: Use vertical - angle relationship for angle 6

Angle 6 and angle 8 are vertical angles. Since angle 6\(\cong\)angle 2, and angle 6\(\cong\)angle 8 (vertical angles), then angle 8\(\cong\)angle 2.

Answer:

Angle 4, Angle 6, Angle 8