Question

given ( mparallel cb ) prove ( mangle abc+mangle bac + mangle acb=180^{circ} ) which statement justifies that angle ( xae ) 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:

• When two parallel lines ($m$ and $CB$) are cut by a transversal ($AB$ in this case for angles $XAB$ and $ABC$), alternate interior angles are formed.
• Alternate interior angles have the following property: If two parallel lines are cut by a transversal, then the alternate interior angles are congruent.
• In the given figure, line $m$ is parallel to line $CB$, and line $AB$ acts as a transversal. Angles $XAB$ and $ABC$ are alternate interior angles. So, the statement “Alternate interior angles of parallel lines cut by a transversal are congruent” justifies that $\angle XAB\cong\angle ABC$.

Answer:

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