Question

given: ( m parallel overline{cb} )
prove: ( m angle abc + m angle bac + m angle acb = 180^circ )
which statement justifies that angle xab is congruent
to angle abc?
○ corresponding angles of parallel lines cut by a
transversal are congruent.
○ vertical angles are congruent
○ same - side interior angles of parallel lines cut by a
transversal are supplementary.
○ alternate interior angles of parallel lines cut by a
transversal are congruent.

Explanation:

• Corresponding angles: These are in the same relative position. \( \angle XAB\) and \( \angle ABC\) are not in corresponding positions.
• Vertical angles: These are opposite angles formed by two intersecting lines. \( \angle XAB\) and \( \angle ABC\) are not formed by two intersecting lines.
• Same - side interior angles: These sum to \(180^{\circ}\). \( \angle XAB\) and \( \angle ABC\) do not sum to \(180^{\circ}\) (we want congruence, not supplementary).
• Alternate interior angles: When two parallel lines (\(m\parallel CB\)) are cut by a transversal (\(AB\)), alternate interior angles are congruent. \( \angle XAB\) and \( \angle ABC\) are alternate interior angles.

Answer:

Alternate interior angles of parallel lines cut by a transversal are congruent.