Transversal cuts parallel lines and at points x and y respectively. the point nearest to c is x, and the point nearest to d is y. points p and r lie on one side of , while q and s lie on the other side. according to the alternate exterior angles theorem, which angle is congruent to ∠cxp? a. ∠ryd b. ∠syd c. ∠cxq d. ∠xys

 The answer is (B) ∠SYD.

Step-by-step explanation: As mentioned in the question, two parallel lines PQ and RS are drawn in the attached figure. The transversal CD cut the lines PQ and RS at the points X and Y respectively.

We are given four angles, out of which one should be chosen which is congruent to ∠CXP.

The angles lying on opposite sides of the transversal and outside the two parallel lines are called alternate exterior angles.

For example, in the figure attached, ∠CXP, ∠SYD and ∠CXQ, ∠RYD are pairs of alternate exterior angles.

Now, the theorem of alternate exterior angles states that if the two lines are parallel having a transversal, then alternate exterior angles are congruent to each other.

Thus, we have

∠CXP ≅ ∠SYD.

So, option (B) is correct.

The answer is (B) ∠SYD.

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