test 4, math section 1, problem 5 "Angles on a wheel"

[irs031]

Problem shows a diagram, which I can't show here.

We are given a wheel of a total of 6 ("vertical"?) angles. 3 angles, marked with variable a are ("vertical"?) with 3 other angles marked with variable b. The only condition given is that a <60. We have to compare a and b.

All of the 3 lines appear to be straight lines and all six angles appear to be vertical angles. I am aware that GRE diagrams should not be trusted, but as far as I know, a line that appears straight on the GRE is in fact straight. If we cross two straight lines to form a letter "X" and then cross that by a third horizontal straight line through the middle of the x, we end up with six vertical angles?

Given that the answer to this question is not C, then these angles are not vertical? However I am having some difficulty grasping how this is even conceptually possible? Let's assume say the horizontal line that crosses the "X" is not straight and points downward after crossing the middle of "X". In this case one of the "a" angles will be larger than the other two, which in turn means that this angle should be marked with a variable different than "a".


Does a line that appear straight on the GRE is actually straight? How is it possible to have six angles that appear vertical, but they are in fact not vertical?

[tommywallach]

You are misusing that term, so I don't understand your question.

You said: "All of the 3 lines appear to be straight lines and all six angles appear to be vertical angles". Nothing can APPEAR to be a vertical angle. It either is one or isn't. So you must think it means something it doesn't.

"Vertical angles" are just whatever angle you get when you cross two lines. It doesn't tell you anything about the angle, it's just a way of describing things, with no numerical meaning (i.e. if I drew two lines crossing and told you the topmost vertical angle was 50 degrees, now you would actually know a value). So I'm guessing you're misusing the term "Vertical angle." Also, this isn't a term on the GRE at all, so I'd remove it from your vocabulary anyway.

So, to be clear, the answers to your questions are as follows:

Question: "Does a line that appear straight on the GRE is actually straight?"
Answer: Yes. Always.

Question: How is it possible to have six angles that appear vertical, but they are in fact not vertical?
Answer: This question doesn't make any sense, because there is no such thing as six vertical angles from three lines. You could have three vertical angles (three pairs, because vertical angles are, by definition PAIRS of angles), but your question still is illogical.

Hope that helps!

-t