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To find the value of x, we can use the fact that the sum of the angles in a triangle is always 180 degrees.
2x + 3x + 10 + 4x - 19 = 180
9x - 9 = 180
9x = 189
x = 21
Now we can substitute x = 21 into the expressions for each angle to find their measures.
First angle: 2x = 2(21) = 42 degrees
Second angle: 3x + 10 = 3(21) + 10 = 73 degrees
Third angle: 4x - 19 = 4(21) - 19 = 65 degrees
The measures of the three angles are 42 degrees, 73 degrees, and 65 degrees.