Question

problem 10: (first taught in lesson 24) given that $overleftrightarrow{ba} parallel overleftrightarrow{dc}$, select which type of angle this pair is and then tell whether it is congruent or supplementary. $angle 1$ and $angle 4$ diagram of a figure with points a, b, d, c, angles labeled 1–8, and parallel line arrows after you pick your answer press go. a b c d e a alternate exterior angles; congruent go

Explanation:

1. Identify the transversal: The line \(AC\) is the transversal cutting the parallel lines \(\overleftrightarrow{BA}\) and \(\overleftrightarrow{DC}\).
2. Classify the angles: \(\angle1\) and \(\angle4\) are on opposite sides of the transversal (\(AC\)) and outside the two parallel lines (\(\overleftrightarrow{BA}\) and \(\overleftrightarrow{DC}\)), so they are alternate exterior angles.
3. Determine congruence/supplementarity: By the Alternate Exterior Angles Theorem, alternate exterior angles formed by a transversal cutting parallel lines are congruent. Thus, \(\angle1\) and \(\angle4\) are congruent.

Answer:

A. Alternate exterior angles; congruent