Answer: The angle sum theorem states that the sum of the three angles in any triangle is always 180 degrees. Therefore, we can use this theorem to find the value of y in the given triangle.
We know that angle A = x, angle B = 120 degrees, and angle C = 20 degrees.
The sum of the three angles in this triangle is:
A + B + C = x + 120 + 20 = x + 140
Since y is outside the triangle on a line to the left of x, we can see that the angle formed by the line containing y and the line containing side AC is a straight angle, which has a measure of 180 degrees.
Therefore, we have:
A + C + y = 180
Substituting the values we know, we get:
x + 20 + y = 180
Solving for y, we get:
y = 160 - x
Therefore, the value of y is 160 degrees minus the measure of angle A (which is x).