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According to the Triangle Angle Sum Theorem, the sum of the angles in a triangle is 180 degrees. Therefore, we have:
2x + 3x + 4x = 180
9x = 180
x = 20
Now we can find the measure of the smallest angle:
2x = 2(20) = 40 degrees
So, the measure of the smallest angle in this triangle is 40 degrees.