Question

problem 12: (first taught in lesson 17) given that $overleftrightarrow{ba} parallel overleftrightarrow{dc}$, select which type of angle this pair is and then tell whether it is congruent or supplementary. $angle 4$ and $angle 5$ a b c d e interior angles on the same side of the transversal; supplementary

Explanation:

1. Identify the transversal: The transversal here is \( \overline{AC} \) (connecting points A and C) which intersects the parallel lines \( \overleftrightarrow{BA} \) and \( \overleftrightarrow{DC} \).
2. Classify the angles: \( \angle 4 \) and \( \angle 5 \) are formed between the parallel lines \( \overleftrightarrow{BA} \) and \( \overleftrightarrow{DC} \) and on the same side of the transversal \( \overline{AC} \), so they are interior angles on the same side of the transversal.
3. Determine the relationship: When two parallel lines are cut by a transversal, interior angles on the same side of the transversal are supplementary (their sum is \( 180^\circ \)). Thus, \( \angle 4 \) and \( \angle 5 \) are supplementary.

Answer:

A. Interior angles on the same side of the transversal; supplementary