As Rich has noted, we can PLUG IN angle measurements for x and y and solve for the value of w.
Let x=70 and y=30.
Insert these values into the figure:
Now insert the rest of the angle measurements, making sure that the angles inside each triangle add up to 180 and that any angles that form a straight line add up to 180:
In the resulting figure, w=20. This is our target.
Now plug x=70 and y=30 into the answers to see which yields our target of 20.
Only
A works:
2x + 2y - 180 = 2*70 + 2*30 - 180 = 20.
The correct answer is
A.
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