Question

question 19 1 pts in the figure below, lines l and m are parallel. which statement is true? <1 and <3 are congruent <1 and <8 are supplementary <2 and <4 are supplementary <6 and <7 are congruent

Explanation:

Step1: Recall parallel - line properties

When two parallel lines \(l\) and \(m\) are cut by a transversal, corresponding angles are congruent, alternate - interior angles are congruent, and same - side interior angles are supplementary.

Step2: Analyze each option

• Option A: ∠1 and ∠3 are neither corresponding, alternate - interior, nor vertical angles. They are not congruent.
• Option B: ∠1 and ∠8 are same - side exterior angles. When two parallel lines are cut by a transversal, same - side exterior angles are supplementary.
• Option C: ∠2 and ∠4 are vertical angles. Vertical angles are congruent, not supplementary.
• Option D: ∠6 and ∠7 are adjacent angles. They are not congruent (they are a linear pair and supplementary).

Answer:

B. ∠1 and ∠8 are supplementary