Question

Given: m || CB

Prove: m∠ABC + m∠BAC + m∠ACB = 180°

A triangle and line are shown. Line m contains points X and Y. Triangle A B C sits on line M at point A. Line m and line segment B C are parallel.

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.

Answer 1

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

Reason: AB is a transversal of the parallel lines m and CB, so ∠XAB and ∠ABC are alternate interior angles and therefore congruent.