Question

1. choose the correct answer.which theorem or postulate shows that ∠6 is supplementary to ∠4?same - side exterior angles theoremsame - side interior angles theoremvertical angles theoremalternate interior angles theorem

Explanation:

• Same - Side Interior Angles Theorem:
• When two parallel lines (\(l\) and \(m\)) are cut by a transversal (\(t\)), same - side interior angles are supplementary.
• \(\angle4\) and \(\angle6\) are on the same side of the transversal \(t\) and inside the two lines \(l\) and \(m\).
• Same - Side Exterior Angles Theorem: This theorem is about angles outside the two parallel lines, and \(\angle4\) and \(\angle6\) are not exterior angles.
• Vertical Angles Theorem: Vertical angles are equal, not supplementary. This theorem is not relevant here as \(\angle4\) and \(\angle6\) are not vertical angles.
• Alternate Interior Angles Theorem: Alternate interior angles are equal. Since \(\angle4\) and \(\angle6\) are not alternate interior angles (alternate interior angles are non - adjacent and on opposite sides of the transversal), this theorem does not apply.

Answer:

Same - Side Interior Angles Theorem