Introduction:
In a triangle, the sum of all three angles is always 180 degrees. In this problem, we are given the ratio of the angles in a triangle as 2:7:11, and we need to find the measure of each angle.

Step 1: Finding the common ratio:
To find the measure of each angle, we first need to determine the common ratio between the given angles. We can do this by adding up the parts of the ratio:
2 + 7 + 11 = 20

Step 2: Finding the measure of each angle:
Now that we have the common ratio, we can find the measure of each angle by multiplying the ratio by the common ratio:
Angle 1 = 2 * (180/20) = 2 * 9 = 18 degrees
Angle 2 = 7 * (180/20) = 7 * 9 = 63 degrees
Angle 3 = 11 * (180/20) = 11 * 9 = 99 degrees

Conclusion:
The measure of the angles in the triangle with a ratio of 2:7:11 is 18 degrees, 63 degrees, and 99 degrees.

Summary:
- The sum of all angles in a triangle is always 180 degrees.
- The given ratio of the angles is 2:7:11.
- The common ratio is found by adding up the parts of the ratio, which in this case is 20.
- The measure of each angle is found by multiplying the ratio by the common ratio.
- The angles in the triangle with a ratio of 2:7:11 are 18 degrees, 63 degrees, and 99 degrees.