Question

In the equation, AB || BC and m2 = m3, what relationship can be deduced between angles 1 and 4?

A) They are supplementary
B) They are complementary
C) They are congruent
D) They are vertical angles

Answer 1

Since AB and BC are parallel lines and angle 2 equals angle 3, angles 1 and 4 are congruent as they are alternate interior angles.

Step-by-step explanation:

If we are given that linesAB and BC are parallel (AB || BC) and also that m2 equals m3 (m2 = m3), we can consider the concept of corresponding angles and alternate interior angles created by the transversal cutting through parallel lines. In this context, angle 1 and angle 4 are alternate interior angles. Since the lines are parallel, the corresponding angles would be equal, and therefore the alternate interior angles are also equal. Hence, angles 1 and 4 are congruent.