Question

Which reason is the justification for the statement that angle 1 ≅ angle 4?

1) 3 lines crossing
2) alternate exterior angles theorem
3) vertical angles theorem
4) given definition of parallel lines

Answer 1

Angle 1 is congruent to angle 4 due to the alternate exterior angles theorem, which states that alternate exterior angles are equal when two parallel lines are intersected by a transversal.

Step-by-step explanation:

The justification for the statement that angle 1 is congruent to angle 4 is alternate exterior angles theorem. When two parallel lines are cut by a transversal, the alternate exterior angles are congruent. This means that if two lines are parallel and they are intersected by a third line (transversal), the angles that are on opposite sides of the transversal and outside the parallel lines are equal in measure.