Which statement justifies that angle XAB is congruent to angle ABC?

A. Corresponding angles of parallel lines cut by a transversal are congruent.
B. Vertical angles are congruent.
C. Same-side interior angles of parallel lines cut by a transversal are supplementary.
D. Alternate interior angles of parallel lines cut by a transversal are congruent.

Given: m || CB

Prove: m∠ABC + m∠BAC + m∠ACB = 180°

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boffeemadrid boffeemadrid · Answer 1 · 2019-03-26T07:40:46+01:00

Answer:

(D)

Step-by-step explanation:

It is given that m || CB as m is the straight line, therefore using the straight line property, we have

∠YAC+∠CAB+∠XAB=180° (1)

Since, m is parallel to BC and AB is transversal, thus

∠XAB=∠ABC(Alternate interior angles of parallel lines cut by a transversal are congruent)

and ∠YAC=∠ACB(Alternate interior angles of parallel lines cut by a transversal are congruent.)

Now, substituting the values of ∠XAB and ∠YAC in equation (1), we have

∠ABC + ∠BAC + ∠ACB = 180°.

Hence proved.

Thus, option (D) is correct.

JeanaShupp JeanaShupp · Answer 2 · 2019-04-16T07:24:00+02:00

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

Step-by-step explanation:

In the given picture m is parallel to CB .

Since m is a straight line and the angle of straight line is 180° .

Therefore, m∠XAB+m∠BAC+m∠YAC=180° ........................ (a)

Also, m is parallel to CB and AB is a transversal and because Alternate interior angles of parallel lines cut by a transversal are congruent.

⇒m∠XAB=m∠ABC and m∠YAC=m∠ACB

Put the values of m∠XAB and m∠YAC in equation (a), we get

m∠ABC + m∠BAC + m∠ACB = 180°.

Hence proved.