How To Solve:
For this problem, we can use the parallelogram proof - Adjacent Angles of a Parallelogram are Supplementary.
This means that two consecutive angles in a parallelogram, such as ∠A and ∠B in your figure, add up to 180°.
Proof:
Suppose AB is considered a transversal and AB || CD*. According to the property of transversal, we know that the interior angles on the same side of a transversal are supplementary. Therefore, ∠A + ∠B = 180°.
We substitute our given information and get 50° + ∠B = 180°. Subtracting 50° from each side, we have ∠B = 130°.
So, the second answer, ∠B = 130°, is correct.
I hope this helps!
* - Opposite sides of a parallelogram are always parallel