Question

1. which of these angles is not congruent to angle 5? 4. what is the value of x?

Explanation:

Step1: Recall angle - congruence rules for parallel lines

When two parallel lines are cut by a transversal, vertical - angles are congruent, corresponding angles are congruent, and alternate - interior and alternate - exterior angles are congruent. In the first diagram, angle 5 has the following congruent angles:

• Angle 1 (corresponding angles), angle 3 (vertical angles), angle 7 (alternate - exterior angles). Angle 4 is not congruent to angle 5.

Step2: Use the property of corresponding angles for parallel lines in the second diagram

If lines \(l\) and \(m\) are parallel and cut by a transversal \(t\), then the corresponding angles are equal. So, \(3x=4x + 19\).

Step3: Solve the equation for \(x\)

Subtract \(3x\) from both sides of the equation \(3x=4x + 19\):
\(0=x + 19\).
Then subtract 19 from both sides to get \(x=-19\).

Answer:

1. Angle 4 is not congruent to angle 5.
2. \(x=-19\)