GMAT Prep2 another geometry problem

[jaydeer44]

Can someone please explain this problem to me? I think I am misunderstanding it. The answer is E. I thought it was D...

For statement 1, if two of the angles are right angles, doesn't that mean that all four angles have to be right, and thus all angles = 90 degrees?

For statement 2, if there are a total of 360 degrees in a quadrilateral, and angle ABC is twice the degree measure of angle BCD, doesn't angle ABC have to = 120 degrees and angle BCD = 60 degrees? if not, can you please illustrate how so?

Thanks!

[jackcrystal]

I think it should be A

whats wrong here?

[Ian Stewart]

Can someone please explain this problem to me? I think I am misunderstanding it. The answer is E. I thought it was D...

For statement 1, if two of the angles are right angles, doesn't that mean that all four angles have to be right, and thus all angles = 90 degrees?

For statement 2, if there are a total of 360 degrees in a quadrilateral, and angle ABC is twice the degree measure of angle BCD, doesn't angle ABC have to = 120 degrees and angle BCD = 60 degrees? if not, can you please illustrate how so?

Thanks!

This problem was recently discussed here:

www.beatthegmat.com/measure-of-interior ... 17001.html

To answer your questions, you can have any combination of angles in a quadrilateral, provided they add to 360. If you draw a rectangle, then erase the top of it and extend only one of the heights, then connect the topmost corners, you should get a shape with a base that looks like a rectangle, but with a 'sloping roof'. The angles can easily be made to be 90-90-45-135 in this way, which is how you can make a quadrilateral with two right angles, and with one angle that is double another (because 90 = 2*45), but which does not contain a 60 degree angle. Or you can have a parallelogram with 60-120-60-120 angles, so both statements together are not sufficient.

[jaydeer44]

thanks! i definitely mixed up the definitions of quadrilateral and parallelogram and thus the confusion