Final answer:
The measures of the angles are 40 degrees, 60 degrees, and 80 degrees.
Step-by-step explanation:
To find the measures of the angles of a triangle that are in a ratio of 2:3:4, we can use the fact that the sum of all angles in a triangle is 180 degrees. Let's assume the angles are 2x, 3x, and 4x. So, we have the equation:
2x + 3x + 4x = 180
Combining like terms, we get:
9x = 180
Dividing both sides by 9, we find:
x = 20
Substituting the value of x back into the angles, we get:
2x = 2(20) = 40 degrees
3x = 3(20) = 60 degrees
4x = 4(20) = 80 degrees