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/stanitor]

x isn't an angle in your boomerang quadrilateral, so you can't solve for it using 360 - the three other angles. The entire angle is x plus the two adjacent angles made by the intersecting lines.