Answer:
C
Step-by-step explanation:
At first glance, it seems like all the answers work. But some careful thinking allows us to find the correct answer.
For this question, we will be using the process of elimination.
First, we can eliminate D, because it does not provide any angles on line d, so we cannot prove that line c is parallel to line d.
Second, we can eliminate A. It seems that the 2 angles makes it so that lines c and d must be parallel, however, that is only true if lines a and b are parallel. Since we don't know whether or not lines a and b are parallel, we cannot prove that lines c and d are parallel, so we can eliminate this choice.
Third, we can eliminate B. Like the diagram in A, this diagram can only prove lines c and d are parallel if lines a and b are parallel, and since we don't know whether or not lines a and b are parallel, we cannot prove tat lines c and d are parallel, so we can eliminate this choice.
We are left with C, so the answer must be C.
Of course, just to make sure, we will also check diagram C. Because the 2 angles provided in the diagram are on line a and none are on line b, we do not need line a to be related to line b in any way, as such we can pretend that line b does not exist in this diagram. We can then see that lines c and d must be parallel for this diagram, or else the angles would not work, so C is correct.
