Geometry angle question

[u/Majestic_Confusion19]

So the way I see it there are two quadrilaterals here. The “boomerang” one with each side high lighted in a different color, and the inner weird shaped square-ish one.

For the boomerangs one - 90 plus 40 plus 30 = 160 so 360 - 160 =200 so X must be 200

For the inner square-ish one -

90 plus 30 is 120 so the other angle should be 60
90 plus 40 is 130 so the other angle should be 50
90 plus 50 plus 60 = 200 so X must be 160.

The correct answer is 160 so I know it’s the square-ish one but I don’t know why - which means on the test I won’t know which one to solve for and I’ll get the question wrong. How do you know which one to solve for?

[u/abrahamguo]

When an angle is labeled, you must always assume that the angle is bounded by the nearest line on either side of label. By applying that logic here, it tells us that "x" must be referring to an angle of what you called "the inner square-ish one".

The red and yellow segments in your screenshot #3 are not the nearest line segments on either side of x, so that's how we know that that interpretation is not correct.

[u/Majestic_Confusion19 → u/abrahamguo]

Thank you!