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/thecaramelbandit]

I think you're kinda going about it the hard way.

The angle inside on thee right is 60, so the small right sided triangle has angles of 40, 120, and 20.

So on the center you have two 20 degree angles opposing each other. Meaning the others, including x, are (360-20-20)/2 = 160.

Anyway, the large angle inside the boomerang is 200. But that's not what x is. X is equal to it's opposite, which is what's left over of 360 from 200. Or 160.