Final answer:
The measure of angle ABC is 50 degrees when the degree measures of the angles of a triangle are represented by 2x, x+10, and 2x-30. We find x by solving the equation formed by setting the sum of the angles equal to 180 degrees.
Step-by-step explanation:
If the degree measures of the angles of a triangle ABC are represented by 2x, x+10, and 2x-30, then we can use the fact that the sum of the angles in any triangle is always 180 degrees. Therefore, we can set up an equation to find the value of x and hence the measure of each angle:
2x + (x + 10) + (2x - 30) = 180
Simplifying this equation:
5x - 20 = 180
Adding 20 to both sides gives us:
5x = 200
Dividing by 5, we find that:
x = 40
Now that we have the value of x, we can find the measure of angle ABC, which is represented by x+10, so:
Angle ABC = x + 10 = 40 + 10 = 50 degrees.