Question

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

Answer 1

Answer:  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.