angle AFC is 60(180-90-30 = 60)
angle ABE is 50(180-90-40 = 50)

Polygon ABDF.

Sum of interior angle of a polygon = (n-2)*180 = (4-2)*180 = 360

For polygon ABDF

angle BAF + AFD + x + ABD = 360
90 + 60 + x + 50 = 360
x = 160

Could also use the remote angle theorem and eliminate a couple of steps. Could start with either the 40deg or 30deg angle, both give the same answer. This shows there are truly multiple ways to arrive at the answer.

We are given the 40deg angle, we can determine the obtuse angle in the same small triangle from the 30-60-90 triangle. (180-60=120)

The remote angle theorem states that the sum of the remote angles equals the exterior angle, so 40+120 = 160. Boom.

Likewise, we could use the 30-60-90 to start, but needs a little more math:
We are given the 30deg angle, we can get the obtuse angle in that small triangle by taking 180-(180-40-90)=130deg.

The remote angle theorem states that the sum of the remote angles equals the exterior angle, so 30+130 = 160. Boom.

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