Answer:
B)
Step-by-step explanation:
First, let's write down what we know based on the Vertical Angle Theorem and the info given by the question:
1. Vertical angle theorem claims that opposite angles are the same, therefore:
2. We know from the problem that:
3. Now for the proofing:
Since x+y = u+w, let us try to cross off the variable u and see if we can get x equaling to w.
We know that y=u, so let us switch out y for another u, allowing the same variable to cross out
x+y = u+w --> x+u = u+w --> x=w
Ok now we know x=w, and recall that w=z. So x would also equal to z!
Let us try to proof z=t:
We know that x=t
But now we also know that x=z (from previous)
Therefore we can substitute the z in for x in x=t and voila z=t!
Try finding out if y=w. No matter how many equations you create, they are not the same. It would not make sense either if you use this equation: x+y = u+w. If w and x are the same then y cannot be anything except being equal to "u". We cannot prove that u is equal to anything else either.
Therefore the answer is B)
