MST 3 question 1 of 20 unintersection

[nruthya.rajagopal]

Lines m and n intersect to the right of the picture.

http://www.manhattanprep.com/gre_images ... /163-1.gif

given angles 2x and 3x degrees.Please refer to the question .

If the lines intersect to the right of the picture, then they must not intersect to the left of the picture. If this is the case, then the sum of 2x and 3x must be greater than 180°. (If this sum were exactly 180°, the lines would be parallel, and thus would not intersect at all; if the sum were less than 180°, the lines would intersect on the left of the picture.)

Therefore 2x + 3x > 180, which solves to x > 36. Therefore, x is greater than 36°.

The correct answer is A.
"If the sum of the angles less than 180, then the lines intersect to the left side" and also for greater than 180 , then the lines intersect to right " explanation is not clear to me. is it because the transversal make acute and obtuse angles with the parallel lines intersecting.
kindly explain.

Thanks
Nruthya

[tommywallach]

Hey Nruthya,

It's hard to explain without pictures. Imagine, for a moment, that the two lines were parallel, and that the other line met them perpendicularly. Obviously 2x + 3x would equal 180. Now imagine that you begin to tilt that line (the one inbetween). Whatever angle you tilt it at, 2x + 3x must equal 180. This is because parallel lines meet a transverse at the same angle, so 2x and 3x are by definition supplementary.

Now, think about what happens if you take the parallel lines and tilt them. Imagine bending them towards each other, so that they will eventually meet to the right. Think about what you'd be doing to 2x and 3x. See how they'd get wider and wider and wider (obtuse)? If you imagine the two lines meeting to the left, you can see that 2x and 3x would get smaller and smaller and smaller (more acute).

Does that help?

-t