The measure of one angle in a triangle is 2x degrees, the second angle is 3x + 10 degrees, and the third angle is 4x - 19 degrees. Find the value of x and the measures of all three angles.

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.