Question

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

Explanation:

Step1: Analyze the relationship between ∠XAB and ∠ABC

We know that line \(m\parallel CB\) and \(AB\) is a transversal.
When two parallel lines are cut by a transversal, the alternate - interior angles are congruent.
For parallel lines \(m\) and \(CB\) and transversal \(AB\), \(\angle XAB\) and \(\angle ABC\) are alternate - interior angles.

Answer:

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