Question

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

Answer 1

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.

Answer 2

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.