If AB || CD, APQ = 50º and PRD =127º. Then the value of x and y is(A) x = 55º and y = 72º(B) x = 50° and y = 77º(C) x = 60º and y = 67º(D) x = 30º and y = 54

To find the values of x and y, we need to use the properties of parallel lines and angles.

Given that AB || CD, we can conclude that the alternate interior angles are congruent. Therefore, ∠APQ = ∠PRD.

We are given that ∠APQ = 50º and ∠PRD = 127º.

Since ∠APQ = ∠PRD, we can set up the equation:

50º = 127º - x

Simplifying the equation, we have:

x = 127º - 50º x = 77º

So, the value of x is 77º.

To find the value of y, we can use the fact that the sum of the angles in a triangle is 180º.

In triangle PRD, we have:

∠PRD + ∠PDR + ∠RDP = 180º

Substituting the given values, we have:

127º + y + 180º - 127º - 50º = 180º

Simplifying the equation, we have:

y + 3º = 180º

y = 180º - 3º y = 177º

So, the value of y is 177º.

Therefore, the correct answer is (B) x = 50° and y = 77º.