Question

given: ( mparallel cb ) prove: ( mangle abc + mangle bac + mangle 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 the same relative position for a transversal - parallel line pair.
• Vertical angles: These are formed by two intersecting lines. \( \angle XAB\) and \( \angle ABC\) are not formed by two intersecting lines.
• Same - side interior angles: These angles are on the same side of the transversal and inside the two parallel lines. Same - side interior angles are supplementary (\(m\angle+\ m\angle = 180^{\circ}\)), not congruent.
• Alternate interior angles: Alternate interior angles are formed when a transversal intersects two parallel lines. The transversal is \(AB\), and the parallel lines are \(m\) and \(CB\). \( \angle XAB\) and \( \angle ABC\) lie between the parallel lines \(m\) and \(CB\) and on opposite sides of the transversal \(AB\).

Answer:

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