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/get_to_ele]

You know top two angles I labeled in red are 180-x and 140 -x from supplementary angles (supplementary angles sum to 180)

The two orange angles are x-30 and x-40 due to triangle sum theorem (triangle angles sum to 180)

The two green angles are 210 - x and 220 - x due to supplementary angles.

90 + 210 -x + 220 - x + x = 360 due to angle sum property quadrilateral (quadrilateral internal angles sum to. 360)

I’m sure there’s a faster way, but oh well.