Question on Math Section of Practice Exam #4

[eliciajohn80]

Hi,

I just completed Practice Exam #4, and I am a bit confused by the answer for the "Angles on a wheel..." problem. For this problem, there are three intersecting lines forming six angles. Three of the angles are measured as "b" and three of the angles are measured as "a." All angles b are opposite to angles a.

It seems as though a=b because the angles are formed when two lines intersect and they are opposite to each other. Therefore, it seems as though the measure of each angle should be 60 degrees.

However, the problem specifies that angle "a" is less than 60 degrees. How is that possible?

I would greatly appreciate clarification. I know there are some things that we cannot assume on the GRE - like the relative size of angles. However, it seemed like assuming that two lines that appear as if they are intersecting are actually intersecting is reasonable. The conclusion about the angles measures comes directing from the assumption that the lines are intersecting.

Thanks,
Elicia

[tommywallach]

Hey Elicia,

So here's the game: these are not three straight lines that go through the center, but six straight lines, all of that meet at the center.

You can know this in two ways. First off, if you just look at the picture, you can see that they aren't straight (particularly the line that goes from the bottom left to the center, then from the center to the top right). More importantly, the very fact that the question has told you that a < 60 is telling you they aren't straight lines. If they were, you'd be right!

Hope that helps!

-t